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StirlingSet

['A048993', 'A008277', 'A008278', 'A080417', 'A106800', 'A151511', 'A151512', 'A154959', 'A213735']

StirlingSet Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, 1, 1]
Row3 [0, 1, 3, 1]
Row4 [0, 1, 7, 6, 1]
Row5 [0, 1, 15, 25, 10, 1]
Row6 [0, 1, 31, 90, 65, 15, 1]
Row7 [0, 1, 63, 301, 350, 140, 21, 1]
Row8 [0, 1, 127, 966, 1701, 1050, 266, 28, 1]
Row9 [0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1]

StirlingSet Triangles

Flat Seq
Triangle [[1], [0, 1], [0, 1, 1], [0, 1, 3, 1], [0, 1, 7, 6, 1], [0, 1, 15, 25, 10, 1], [0, 1, 31, 90, 65, 15, 1], [0, 1, 63, 301, 350, 140, 21, 1], [0, 1, 127, 966, 1701, 1050, 266, 28, 1], [0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1]]
RevTabl [[1], [1, 0], [1, 1, 0], [1, 3, 1, 0], [1, 6, 7, 1, 0], [1, 10, 25, 15, 1, 0], [1, 15, 65, 90, 31, 1, 0], [1, 21, 140, 350, 301, 63, 1, 0], [1, 28, 266, 1050, 1701, 966, 127, 1, 0], [1, 36, 462, 2646, 6951, 7770, 3025, 255, 1, 0]]
AntiDiag [[1], [0], [0, 1], [0, 1], [0, 1, 1], [0, 1, 3], [0, 1, 7, 1], [0, 1, 15, 6], [0, 1, 31, 25, 1], [0, 1, 63, 90, 10]]
AccTabl [[1], [0, 1], [0, 1, 2], [0, 1, 4, 5], [0, 1, 8, 14, 15], [0, 1, 16, 41, 51, 52], [0, 1, 32, 122, 187, 202, 203], [0, 1, 64, 365, 715, 855, 876, 877], [0, 1, 128, 1094, 2795, 3845, 4111, 4139, 4140], [0, 1, 256, 3281, 11051, 18002, 20648, 21110, 21146, 21147]]
RevAccTabl [[1], [1, 0], [2, 1, 0], [5, 4, 1, 0], [15, 14, 8, 1, 0], [52, 51, 41, 16, 1, 0], [203, 202, 187, 122, 32, 1, 0], [877, 876, 855, 715, 365, 64, 1, 0], [4140, 4139, 4111, 3845, 2795, 1094, 128, 1, 0], [21147, 21146, 21110, 20648, 18002, 11051, 3281, 256, 1, 0]]
AccRevTabl [[1], [1, 1], [1, 2, 2], [1, 4, 5, 5], [1, 7, 14, 15, 15], [1, 11, 36, 51, 52, 52], [1, 16, 81, 171, 202, 203, 203], [1, 22, 162, 512, 813, 876, 877, 877], [1, 29, 295, 1345, 3046, 4012, 4139, 4140, 4140], [1, 37, 499, 3145, 10096, 17866, 20891, 21146, 21147, 21147]]
DiffxTabl [[1], [0, 2], [0, 2, 3], [0, 2, 9, 4], [0, 2, 21, 24, 5], [0, 2, 45, 100, 50, 6], [0, 2, 93, 360, 325, 90, 7], [0, 2, 189, 1204, 1750, 840, 147, 8], [0, 2, 381, 3864, 8505, 6300, 1862, 224, 9], [0, 2, 765, 12100, 38850, 41706, 18522, 3696, 324, 10]]

StirlingSet Row sums

Trait Seq
RowSum [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
EvenSum [1, 0, 1, 3, 8, 25, 97, 434, 2095, 10707]
OddSum [0, 1, 1, 2, 7, 27, 106, 443, 2045, 10440]
AltSum [1, -1, 0, 1, 1, -2, -9, -9, 50, 267]
AbsSum [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
AccSum [1, 1, 3, 10, 38, 161, 747, 3753, 20253, 116642]
AccRevSum [1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975]
DiagSum [1, 0, 1, 1, 2, 4, 9, 22, 58, 164]

StirlingSet Transforms

Trans Seq
RowLcm [1, 1, 1, 3, 42, 150, 36270, 270900, 9440379900, 3332912051700]
RowGcd [1, 1, 1, 3, 1, 5, 1, 7, 1, 1]
RowMax [1, 1, 1, 3, 7, 25, 90, 350, 1701, 7770]
CentralE [1, 1, 7, 90, 1701]
CentralO [0, 1, 15, 301, 7770]
ColMiddle [1, 0, 1, 1, 7, 15, 90, 301, 1701, 7770]
ColLeft [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 1, 3, 13, 71, 456, 3337, 27203, 243203, 2357356]
InvBinConv [1, 1, -1, -5, 15, 56, -455, -237, 16947, -64220]
TransSqrs [0, 1, 5, 22, 99, 471, 2386, 12867, 73681, 446620]
TransNat0 [0, 1, 3, 10, 37, 151, 674, 3263, 17007, 94828]
TransNat1 [1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975]
PosHalf [1, 1, 3, 11, 49, 257, 1539, 10299, 75905, 609441]
NegHalf [1, 1, -1, -1, 9, -23, -25, 583, -3087, 4401]

StirlingSet Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, 1, 3, 6, 10, 15, 21, 28, 36, 45]
DiagRow2 [0, 1, 7, 25, 65, 140, 266, 462, 750, 1155]
DiagRow3 [0, 1, 15, 90, 350, 1050, 2646, 5880, 11880, 22275]
DiagRow4 [0, 1, 31, 301, 1701, 6951, 22827, 63987, 159027, 359502]
DiagRow5 [0, 1, 63, 966, 7770, 42525, 179487, 627396, 1899612, 5135130]
DiagRow6 [0, 1, 127, 3025, 34105, 246730, 1323652, 5715424, 20912320, 67128490]
DiagRow7 [0, 1, 255, 9330, 145750, 1379400, 9321312, 49329280, 216627840, 820784250]
DiagRow8 [0, 1, 511, 28501, 611501, 7508501, 63436373, 408741333, 2141764053, 9528822303]
DiagRow9 [0, 1, 1023, 86526, 2532530, 40075035, 420693273, 3281882604, 20415995028, 106175395755]

StirlingSet Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol2 [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023]
DiagCol3 [1, 6, 25, 90, 301, 966, 3025, 9330, 28501, 86526]
DiagCol4 [1, 10, 65, 350, 1701, 7770, 34105, 145750, 611501, 2532530]
DiagCol5 [1, 15, 140, 1050, 6951, 42525, 246730, 1379400, 7508501, 40075035]
DiagCol6 [1, 21, 266, 2646, 22827, 179487, 1323652, 9321312, 63436373, 420693273]
DiagCol7 [1, 28, 462, 5880, 63987, 627396, 5715424, 49329280, 408741333, 3281882604]
DiagCol8 [1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141764053, 20415995028]
DiagCol9 [1, 45, 1155, 22275, 359502, 5135130, 67128490, 820784250, 9528822303, 106175395755]

StirlingSet Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2 [0, 2, 6, 12, 20, 30, 42, 56, 72, 90]
PolyRow3 [0, 5, 22, 57, 116, 205, 330, 497, 712, 981]
PolyRow4 [0, 15, 94, 309, 756, 1555, 2850, 4809, 7624, 11511]
PolyRow5 [0, 52, 454, 1866, 5428, 12880, 26682, 50134, 87496, 144108]
PolyRow6 [0, 203, 2430, 12351, 42356, 115155, 268098, 558215, 1067976, 1911771]
PolyRow7 [0, 877, 14214, 88563, 355636, 1101705, 2869242, 6593839, 13781448, 26730981]
PolyRow8 [0, 4140, 89918, 681870, 3188340, 11202680, 32510850, 82187658, 187104200, 392209380]
PolyRow9 [0, 21147, 610182, 5597643, 30333492, 120415755, 388109562, 1076193867, 2661876168, 6016681467]

StirlingSet Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
PolyCol2 [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182]
PolyCol3 [1, 3, 12, 57, 309, 1866, 12351, 88563, 681870, 5597643]
PolyCol4 [1, 4, 20, 116, 756, 5428, 42356, 355636, 3188340, 30333492]
PolyCol5 [1, 5, 30, 205, 1555, 12880, 115155, 1101705, 11202680, 120415755]
PolyCol6 [1, 6, 42, 330, 2850, 26682, 268098, 2869242, 32510850, 388109562]
PolyCol7 [1, 7, 56, 497, 4809, 50134, 558215, 6593839, 82187658, 1076193867]
PolyCol8 [1, 8, 72, 712, 7624, 87496, 1067976, 13781448, 187104200, 2661876168]
PolyCol9 [1, 9, 90, 981, 11511, 144108, 1911771, 26730981, 392209380, 6016681467]

StirlingSet:Inv

[]

StirlingSet:Inv Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, -1, 1]
Row3 [0, 2, -3, 1]
Row4 [0, -6, 11, -6, 1]
Row5 [0, 24, -50, 35, -10, 1]
Row6 [0, -120, 274, -225, 85, -15, 1]
Row7 [0, 720, -1764, 1624, -735, 175, -21, 1]
Row8 [0, -5040, 13068, -13132, 6769, -1960, 322, -28, 1]
Row9 [0, 40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1]

StirlingSet:Inv Triangles

Flat Seq
Triangle [[1], [0, 1], [0, -1, 1], [0, 2, -3, 1], [0, -6, 11, -6, 1], [0, 24, -50, 35, -10, 1], [0, -120, 274, -225, 85, -15, 1], [0, 720, -1764, 1624, -735, 175, -21, 1], [0, -5040, 13068, -13132, 6769, -1960, 322, -28, 1], [0, 40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1]]
RevTabl [[1], [1, 0], [1, -1, 0], [1, -3, 2, 0], [1, -6, 11, -6, 0], [1, -10, 35, -50, 24, 0], [1, -15, 85, -225, 274, -120, 0], [1, -21, 175, -735, 1624, -1764, 720, 0], [1, -28, 322, -1960, 6769, -13132, 13068, -5040, 0], [1, -36, 546, -4536, 22449, -67284, 118124, -109584, 40320, 0]]
AntiDiag [[1], [0], [0, 1], [0, -1], [0, 2, 1], [0, -6, -3], [0, 24, 11, 1], [0, -120, -50, -6], [0, 720, 274, 35, 1], [0, -5040, -1764, -225, -10]]
AccTabl [[1], [0, 1], [0, -1, 0], [0, 2, -1, 0], [0, -6, 5, -1, 0], [0, 24, -26, 9, -1, 0], [0, -120, 154, -71, 14, -1, 0], [0, 720, -1044, 580, -155, 20, -1, 0], [0, -5040, 8028, -5104, 1665, -295, 27, -1, 0], [0, 40320, -69264, 48860, -18424, 4025, -511, 35, -1, 0]]
RevAccTabl [[1], [1, 0], [0, -1, 0], [0, -1, 2, 0], [0, -1, 5, -6, 0], [0, -1, 9, -26, 24, 0], [0, -1, 14, -71, 154, -120, 0], [0, -1, 20, -155, 580, -1044, 720, 0], [0, -1, 27, -295, 1665, -5104, 8028, -5040, 0], [0, -1, 35, -511, 4025, -18424, 48860, -69264, 40320, 0]]
AccRevTabl [[1], [1, 1], [1, 0, 0], [1, -2, 0, 0], [1, -5, 6, 0, 0], [1, -9, 26, -24, 0, 0], [1, -14, 71, -154, 120, 0, 0], [1, -20, 155, -580, 1044, -720, 0, 0], [1, -27, 295, -1665, 5104, -8028, 5040, 0, 0], [1, -35, 511, -4025, 18424, -48860, 69264, -40320, 0, 0]]
DiffxTabl [[1], [0, 2], [0, -2, 3], [0, 4, -9, 4], [0, -12, 33, -24, 5], [0, 48, -150, 140, -50, 6], [0, -240, 822, -900, 425, -90, 7], [0, 1440, -5292, 6496, -3675, 1050, -147, 8], [0, -10080, 39204, -52528, 33845, -11760, 2254, -224, 9], [0, 80640, -328752, 472496, -336420, 134694, -31752, 4368, -324, 10]]

StirlingSet:Inv Row sums

Trait Seq
RowSum [1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
EvenSum [1, 0, 1, -3, 12, -60, 360, -2520, 20160, -181440]
OddSum [0, 1, -1, 3, -12, 60, -360, 2520, -20160, 181440]
AltSum [1, -1, 2, -6, 24, -120, 720, -5040, 40320, -362880]
AbsSum [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
AccSum [1, 1, -1, 1, -2, 6, -24, 120, -720, 5040]
AccRevSum [1, 2, 1, -1, 2, -6, 24, -120, 720, -5040]
DiagSum [1, 0, 1, -1, 3, -9, 36, -176, 1030, -7039]

StirlingSet:Inv Transforms

Trans Seq
RowLcm [1, 1, 1, 6, 66, 4200, 4192200, 5115600, 19083776176080, 10086416728304192640]
RowGcd [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 1, 3, 11, 50, 274, 1764, 13132, 118124]
CentralE [1, -1, 11, -225, 6769]
CentralO [0, 2, -50, 1624, -67284]
ColMiddle [1, 0, -1, 2, 11, -50, -225, 1624, 6769, -67284]
ColLeft [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv [1, 1, -1, -2, 19, -79, 76, 2640, -36945, 329371]
InvBinConv [1, 1, 3, 16, 115, 1021, 10696, 128472, 1734447, 25937683]
TransSqrs [0, 1, 3, -1, 0, 4, -28, 188, -1368, 11016]
TransNat0 [0, 1, 1, -1, 2, -6, 24, -120, 720, -5040]
TransNat1 [1, 2, 1, -1, 2, -6, 24, -120, 720, -5040]
PosHalf [1, 1, -1, 3, -15, 105, -945, 10395, -135135, 2027025]
NegHalf [1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425]

StirlingSet:Inv Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, -1, -3, -6, -10, -15, -21, -28, -36, -45]
DiagRow2 [0, 2, 11, 35, 85, 175, 322, 546, 870, 1320]
DiagRow3 [0, -6, -50, -225, -735, -1960, -4536, -9450, -18150, -32670]
DiagRow4 [0, 24, 274, 1624, 6769, 22449, 63273, 157773, 357423, 749463]
DiagRow5 [0, -120, -1764, -13132, -67284, -269325, -902055, -2637558, -6926634, -16669653]
DiagRow6 [0, 720, 13068, 118124, 723680, 3416930, 13339535, 44990231, 135036473, 368411615]
DiagRow7 [0, -5040, -109584, -1172700, -8409500, -45995730, -206070150, -790943153, -2681453775, -8207628000]
DiagRow8 [0, 40320, 1026576, 12753576, 105258076, 657206836, 3336118786, 14409322928, 54631129553, 185953177553]
DiagRow9 [0, -362880, -10628640, -150917976, -1414014888, -9957703756, -56663366760, -272803210680, -1146901283528, -4308105301929]

StirlingSet:Inv Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, -1, 2, -6, 24, -120, 720, -5040, 40320, -362880]
DiagCol2 [1, -3, 11, -50, 274, -1764, 13068, -109584, 1026576, -10628640]
DiagCol3 [1, -6, 35, -225, 1624, -13132, 118124, -1172700, 12753576, -150917976]
DiagCol4 [1, -10, 85, -735, 6769, -67284, 723680, -8409500, 105258076, -1414014888]
DiagCol5 [1, -15, 175, -1960, 22449, -269325, 3416930, -45995730, 657206836, -9957703756]
DiagCol6 [1, -21, 322, -4536, 63273, -902055, 13339535, -206070150, 3336118786, -56663366760]
DiagCol7 [1, -28, 546, -9450, 157773, -2637558, 44990231, -790943153, 14409322928, -272803210680]
DiagCol8 [1, -36, 870, -18150, 357423, -6926634, 135036473, -2681453775, 54631129553, -1146901283528]
DiagCol9 [1, -45, 1320, -32670, 749463, -16669653, 368411615, -8207628000, 185953177553, -4308105301929]

StirlingSet:Inv Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2 [0, 0, 2, 6, 12, 20, 30, 42, 56, 72]
PolyRow3 [0, 0, 0, 6, 24, 60, 120, 210, 336, 504]
PolyRow4 [0, 0, 0, 0, 24, 120, 360, 840, 1680, 3024]
PolyRow5 [0, 0, 0, 0, 0, 120, 720, 2520, 6720, 15120]
PolyRow6 [0, 0, 0, 0, 0, 0, 720, 5040, 20160, 60480]
PolyRow7 [0, 0, 0, 0, 0, 0, 0, 5040, 40320, 181440]
PolyRow8 [0, 0, 0, 0, 0, 0, 0, 0, 40320, 362880]
PolyRow9 [0, 0, 0, 0, 0, 0, 0, 0, 0, 362880]

StirlingSet:Inv Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol2 [1, 2, 2, 0, 0, 0, 0, 0, 0, 0]
PolyCol3 [1, 3, 6, 6, 0, 0, 0, 0, 0, 0]
PolyCol4 [1, 4, 12, 24, 24, 0, 0, 0, 0, 0]
PolyCol5 [1, 5, 20, 60, 120, 120, 0, 0, 0, 0]
PolyCol6 [1, 6, 30, 120, 360, 720, 720, 0, 0, 0]
PolyCol7 [1, 7, 42, 210, 840, 2520, 5040, 5040, 0, 0]
PolyCol8 [1, 8, 56, 336, 1680, 6720, 20160, 40320, 40320, 0]
PolyCol9 [1, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 362880]

StirlingSet:Rev

[]

StirlingSet:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, 1, 0]
Row3 [1, 3, 1, 0]
Row4 [1, 6, 7, 1, 0]
Row5 [1, 10, 25, 15, 1, 0]
Row6 [1, 15, 65, 90, 31, 1, 0]
Row7 [1, 21, 140, 350, 301, 63, 1, 0]
Row8 [1, 28, 266, 1050, 1701, 966, 127, 1, 0]
Row9 [1, 36, 462, 2646, 6951, 7770, 3025, 255, 1, 0]

StirlingSet:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, 1, 0], [1, 3, 1, 0], [1, 6, 7, 1, 0], [1, 10, 25, 15, 1, 0], [1, 15, 65, 90, 31, 1, 0], [1, 21, 140, 350, 301, 63, 1, 0], [1, 28, 266, 1050, 1701, 966, 127, 1, 0], [1, 36, 462, 2646, 6951, 7770, 3025, 255, 1, 0]]
RevTabl [[1], [0, 1], [0, 1, 1], [0, 1, 3, 1], [0, 1, 7, 6, 1], [0, 1, 15, 25, 10, 1], [0, 1, 31, 90, 65, 15, 1], [0, 1, 63, 301, 350, 140, 21, 1], [0, 1, 127, 966, 1701, 1050, 266, 28, 1], [0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1]]
AntiDiag [[1], [1], [1, 0], [1, 1], [1, 3, 0], [1, 6, 1], [1, 10, 7, 0], [1, 15, 25, 1], [1, 21, 65, 15, 0], [1, 28, 140, 90, 1]]
AccTabl [[1], [1, 1], [1, 2, 2], [1, 4, 5, 5], [1, 7, 14, 15, 15], [1, 11, 36, 51, 52, 52], [1, 16, 81, 171, 202, 203, 203], [1, 22, 162, 512, 813, 876, 877, 877], [1, 29, 295, 1345, 3046, 4012, 4139, 4140, 4140], [1, 37, 499, 3145, 10096, 17866, 20891, 21146, 21147, 21147]]
RevAccTabl [[1], [1, 1], [2, 2, 1], [5, 5, 4, 1], [15, 15, 14, 7, 1], [52, 52, 51, 36, 11, 1], [203, 203, 202, 171, 81, 16, 1], [877, 877, 876, 813, 512, 162, 22, 1], [4140, 4140, 4139, 4012, 3046, 1345, 295, 29, 1], [21147, 21147, 21146, 20891, 17866, 10096, 3145, 499, 37, 1]]
AccRevTabl [[1], [0, 1], [0, 1, 2], [0, 1, 4, 5], [0, 1, 8, 14, 15], [0, 1, 16, 41, 51, 52], [0, 1, 32, 122, 187, 202, 203], [0, 1, 64, 365, 715, 855, 876, 877], [0, 1, 128, 1094, 2795, 3845, 4111, 4139, 4140], [0, 1, 256, 3281, 11051, 18002, 20648, 21110, 21146, 21147]]
DiffxTabl [[1], [1, 0], [1, 2, 0], [1, 6, 3, 0], [1, 12, 21, 4, 0], [1, 20, 75, 60, 5, 0], [1, 30, 195, 360, 155, 6, 0], [1, 42, 420, 1400, 1505, 378, 7, 0], [1, 56, 798, 4200, 8505, 5796, 889, 8, 0], [1, 72, 1386, 10584, 34755, 46620, 21175, 2040, 9, 0]]

StirlingSet:Rev Row sums

Trait Seq
RowSum [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
EvenSum [1, 1, 1, 2, 8, 27, 97, 443, 2095, 10440]
OddSum [0, 0, 1, 3, 7, 25, 106, 434, 2045, 10707]
AltSum [1, 1, 0, -1, 1, 2, -9, 9, 50, -267]
AbsSum [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
AccSum [1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975]
AccRevSum [1, 1, 3, 10, 38, 161, 747, 3753, 20253, 116642]
DiagSum [1, 1, 1, 2, 4, 8, 18, 42, 102, 260]

StirlingSet:Rev Transforms

Trans Seq
RowLcm [1, 1, 1, 3, 42, 150, 36270, 270900, 9440379900, 3332912051700]
RowGcd [1, 1, 1, 3, 1, 5, 1, 7, 1, 1]
RowMax [1, 1, 1, 3, 7, 25, 90, 350, 1701, 7770]
CentralE [1, 1, 7, 90, 1701]
CentralO [1, 3, 25, 350, 6951]
ColMiddle [1, 1, 1, 3, 7, 25, 90, 350, 1701, 6951]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [1, 1, 3, 13, 71, 456, 3337, 27203, 243203, 2357356]
InvBinConv [1, -1, -1, 5, 15, -56, -455, 237, 16947, 64220]
TransSqrs [0, 0, 1, 7, 43, 261, 1606, 10158, 66529, 452623]
TransNat0 [0, 0, 1, 5, 23, 109, 544, 2876, 16113, 95495]
TransNat1 [1, 1, 3, 10, 38, 161, 747, 3753, 20253, 116642]
PosHalf [1, 2, 6, 22, 94, 454, 2430, 14214, 89918, 610182]
NegHalf [1, -2, 2, 2, -6, -14, 26, 178, 90, -2382]

StirlingSet:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow2 [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023]
DiagRow3 [1, 6, 25, 90, 301, 966, 3025, 9330, 28501, 86526]
DiagRow4 [1, 10, 65, 350, 1701, 7770, 34105, 145750, 611501, 2532530]
DiagRow5 [1, 15, 140, 1050, 6951, 42525, 246730, 1379400, 7508501, 40075035]
DiagRow6 [1, 21, 266, 2646, 22827, 179487, 1323652, 9321312, 63436373, 420693273]
DiagRow7 [1, 28, 462, 5880, 63987, 627396, 5715424, 49329280, 408741333, 3281882604]
DiagRow8 [1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141764053, 20415995028]
DiagRow9 [1, 45, 1155, 22275, 359502, 5135130, 67128490, 820784250, 9528822303, 106175395755]

StirlingSet:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, 1, 3, 6, 10, 15, 21, 28, 36, 45]
DiagCol2 [0, 1, 7, 25, 65, 140, 266, 462, 750, 1155]
DiagCol3 [0, 1, 15, 90, 350, 1050, 2646, 5880, 11880, 22275]
DiagCol4 [0, 1, 31, 301, 1701, 6951, 22827, 63987, 159027, 359502]
DiagCol5 [0, 1, 63, 966, 7770, 42525, 179487, 627396, 1899612, 5135130]
DiagCol6 [0, 1, 127, 3025, 34105, 246730, 1323652, 5715424, 20912320, 67128490]
DiagCol7 [0, 1, 255, 9330, 145750, 1379400, 9321312, 49329280, 216627840, 820784250]
DiagCol8 [0, 1, 511, 28501, 611501, 7508501, 63436373, 408741333, 2141764053, 9528822303]
DiagCol9 [0, 1, 1023, 86526, 2532530, 40075035, 420693273, 3281882604, 20415995028, 106175395755]

StirlingSet:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
PolyRow3 [1, 5, 11, 19, 29, 41, 55, 71, 89, 109]
PolyRow4 [1, 15, 49, 109, 201, 331, 505, 729, 1009, 1351]
PolyRow5 [1, 52, 257, 742, 1657, 3176, 5497, 8842, 13457, 19612]
PolyRow6 [1, 203, 1539, 5815, 15821, 35451, 69823, 125399, 210105, 333451]
PolyRow7 [1, 877, 10299, 51193, 170389, 447981, 1007407, 2026249, 3747753, 6493069]
PolyRow8 [1, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473, 141264820]
PolyRow9 [1, 21147, 609441, 5296321, 26546673, 96546231, 284214097, 719866701, 1628999841, 3376695763]

StirlingSet:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]
PolyCol2 [1, 1, 3, 11, 49, 257, 1539, 10299, 75905, 609441]
PolyCol3 [1, 1, 4, 19, 109, 742, 5815, 51193, 498118, 5296321]
PolyCol4 [1, 1, 5, 29, 201, 1657, 15821, 170389, 2032785, 26546673]
PolyCol5 [1, 1, 6, 41, 331, 3176, 35451, 447981, 6282416, 96546231]
PolyCol6 [1, 1, 7, 55, 505, 5497, 69823, 1007407, 16157905, 284214097]
PolyCol7 [1, 1, 8, 71, 729, 8842, 125399, 2026249, 36458010, 719866701]
PolyCol8 [1, 1, 9, 89, 1009, 13457, 210105, 3747753, 74565473, 1628999841]
PolyCol9 [1, 1, 10, 109, 1351, 19612, 333451, 6493069, 141264820, 3376695763]

StirlingSet:Inv:Rev

[]

StirlingSet:Inv:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, -1, 0]
Row3 [1, -3, 2, 0]
Row4 [1, -6, 11, -6, 0]
Row5 [1, -10, 35, -50, 24, 0]
Row6 [1, -15, 85, -225, 274, -120, 0]
Row7 [1, -21, 175, -735, 1624, -1764, 720, 0]
Row8 [1, -28, 322, -1960, 6769, -13132, 13068, -5040, 0]
Row9 [1, -36, 546, -4536, 22449, -67284, 118124, -109584, 40320, 0]

StirlingSet:Inv:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, -1, 0], [1, -3, 2, 0], [1, -6, 11, -6, 0], [1, -10, 35, -50, 24, 0], [1, -15, 85, -225, 274, -120, 0], [1, -21, 175, -735, 1624, -1764, 720, 0], [1, -28, 322, -1960, 6769, -13132, 13068, -5040, 0], [1, -36, 546, -4536, 22449, -67284, 118124, -109584, 40320, 0]]
RevTabl [[1], [0, 1], [0, -1, 1], [0, 2, -3, 1], [0, -6, 11, -6, 1], [0, 24, -50, 35, -10, 1], [0, -120, 274, -225, 85, -15, 1], [0, 720, -1764, 1624, -735, 175, -21, 1], [0, -5040, 13068, -13132, 6769, -1960, 322, -28, 1], [0, 40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1]]
AntiDiag [[1], [1], [1, 0], [1, -1], [1, -3, 0], [1, -6, 2], [1, -10, 11, 0], [1, -15, 35, -6], [1, -21, 85, -50, 0], [1, -28, 175, -225, 24]]
AccTabl [[1], [1, 1], [1, 0, 0], [1, -2, 0, 0], [1, -5, 6, 0, 0], [1, -9, 26, -24, 0, 0], [1, -14, 71, -154, 120, 0, 0], [1, -20, 155, -580, 1044, -720, 0, 0], [1, -27, 295, -1665, 5104, -8028, 5040, 0, 0], [1, -35, 511, -4025, 18424, -48860, 69264, -40320, 0, 0]]
RevAccTabl [[1], [1, 1], [0, 0, 1], [0, 0, -2, 1], [0, 0, 6, -5, 1], [0, 0, -24, 26, -9, 1], [0, 0, 120, -154, 71, -14, 1], [0, 0, -720, 1044, -580, 155, -20, 1], [0, 0, 5040, -8028, 5104, -1665, 295, -27, 1], [0, 0, -40320, 69264, -48860, 18424, -4025, 511, -35, 1]]
AccRevTabl [[1], [0, 1], [0, -1, 0], [0, 2, -1, 0], [0, -6, 5, -1, 0], [0, 24, -26, 9, -1, 0], [0, -120, 154, -71, 14, -1, 0], [0, 720, -1044, 580, -155, 20, -1, 0], [0, -5040, 8028, -5104, 1665, -295, 27, -1, 0], [0, 40320, -69264, 48860, -18424, 4025, -511, 35, -1, 0]]
DiffxTabl [[1], [1, 0], [1, -2, 0], [1, -6, 6, 0], [1, -12, 33, -24, 0], [1, -20, 105, -200, 120, 0], [1, -30, 255, -900, 1370, -720, 0], [1, -42, 525, -2940, 8120, -10584, 5040, 0], [1, -56, 966, -7840, 33845, -78792, 91476, -40320, 0], [1, -72, 1638, -18144, 112245, -403704, 826868, -876672, 362880, 0]]

StirlingSet:Inv:Rev Row sums

Trait Seq
RowSum [1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
EvenSum [1, 1, 1, 3, 12, 60, 360, 2520, 20160, 181440]
OddSum [0, 0, -1, -3, -12, -60, -360, -2520, -20160, -181440]
AltSum [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
AbsSum [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
AccSum [1, 2, 1, -1, 2, -6, 24, -120, 720, -5040]
AccRevSum [1, 1, -1, 1, -2, 6, -24, 120, -720, 5040]
DiagSum [1, 1, 1, 0, -2, -3, 2, 15, 15, -53]

StirlingSet:Inv:Rev Transforms

Trans Seq
RowLcm [1, 1, 1, 6, 66, 4200, 4192200, 5115600, 19083776176080, 10086416728304192640]
RowGcd [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
RowMax [1, 1, 1, 3, 11, 50, 274, 1764, 13132, 118124]
CentralE [1, -1, 11, -225, 6769]
CentralO [1, -3, 35, -735, 22449]
ColMiddle [1, 1, -1, -3, 11, 35, -225, -735, 6769, 22449]
ColLeft [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [1, 1, -1, -2, 19, -79, 76, 2640, -36945, 329371]
InvBinConv [1, -1, 3, -16, 115, -1021, 10696, -128472, 1734447, -25937683]
TransSqrs [0, 0, -1, 5, -16, 64, -316, 1868, -12888, 101736]
TransNat0 [0, 0, -1, 1, -2, 6, -24, 120, -720, 5040]
TransNat1 [1, 1, -1, 1, -2, 6, -24, 120, -720, 5040]
PosHalf [1, 2, 2, 0, 0, 0, 0, 0, 0, 0]
NegHalf [1, -2, 6, -24, 120, -720, 5040, -40320, 362880, -3628800]

StirlingSet:Inv:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, -1, 2, -6, 24, -120, 720, -5040, 40320, -362880]
DiagRow2 [1, -3, 11, -50, 274, -1764, 13068, -109584, 1026576, -10628640]
DiagRow3 [1, -6, 35, -225, 1624, -13132, 118124, -1172700, 12753576, -150917976]
DiagRow4 [1, -10, 85, -735, 6769, -67284, 723680, -8409500, 105258076, -1414014888]
DiagRow5 [1, -15, 175, -1960, 22449, -269325, 3416930, -45995730, 657206836, -9957703756]
DiagRow6 [1, -21, 322, -4536, 63273, -902055, 13339535, -206070150, 3336118786, -56663366760]
DiagRow7 [1, -28, 546, -9450, 157773, -2637558, 44990231, -790943153, 14409322928, -272803210680]
DiagRow8 [1, -36, 870, -18150, 357423, -6926634, 135036473, -2681453775, 54631129553, -1146901283528]
DiagRow9 [1, -45, 1320, -32670, 749463, -16669653, 368411615, -8207628000, 185953177553, -4308105301929]

StirlingSet:Inv:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, -1, -3, -6, -10, -15, -21, -28, -36, -45]
DiagCol2 [0, 2, 11, 35, 85, 175, 322, 546, 870, 1320]
DiagCol3 [0, -6, -50, -225, -735, -1960, -4536, -9450, -18150, -32670]
DiagCol4 [0, 24, 274, 1624, 6769, 22449, 63273, 157773, 357423, 749463]
DiagCol5 [0, -120, -1764, -13132, -67284, -269325, -902055, -2637558, -6926634, -16669653]
DiagCol6 [0, 720, 13068, 118124, 723680, 3416930, 13339535, 44990231, 135036473, 368411615]
DiagCol7 [0, -5040, -109584, -1172700, -8409500, -45995730, -206070150, -790943153, -2681453775, -8207628000]
DiagCol8 [0, 40320, 1026576, 12753576, 105258076, 657206836, 3336118786, 14409322928, 54631129553, 185953177553]
DiagCol9 [0, -362880, -10628640, -150917976, -1414014888, -9957703756, -56663366760, -272803210680, -1146901283528, -4308105301929]

StirlingSet:Inv:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2 [1, 0, -1, -2, -3, -4, -5, -6, -7, -8]
PolyRow3 [1, 0, 3, 10, 21, 36, 55, 78, 105, 136]
PolyRow4 [1, 0, -15, -80, -231, -504, -935, -1560, -2415, -3536]
PolyRow5 [1, 0, 105, 880, 3465, 9576, 21505, 42120, 74865, 123760]
PolyRow6 [1, 0, -945, -12320, -65835, -229824, -623645, -1432080, -2919735, -5445440]
PolyRow7 [1, 0, 10395, 209440, 1514205, 6664896, 21827575, 58715280, 137227545, 288608320]
PolyRow8 [1, 0, -135135, -4188800, -40883535, -226606464, -894930575, -2818333440, -7547514975, -17893715840]
PolyRow9 [1, 0, 2027025, 96342400, 1267389585, 8837652096, 42061737025, 155008339200, 475493443425, 1270453824640]

StirlingSet:Inv:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol2 [1, 1, -1, 3, -15, 105, -945, 10395, -135135, 2027025]
PolyCol3 [1, 1, -2, 10, -80, 880, -12320, 209440, -4188800, 96342400]
PolyCol4 [1, 1, -3, 21, -231, 3465, -65835, 1514205, -40883535, 1267389585]
PolyCol5 [1, 1, -4, 36, -504, 9576, -229824, 6664896, -226606464, 8837652096]
PolyCol6 [1, 1, -5, 55, -935, 21505, -623645, 21827575, -894930575, 42061737025]
PolyCol7 [1, 1, -6, 78, -1560, 42120, -1432080, 58715280, -2818333440, 155008339200]
PolyCol8 [1, 1, -7, 105, -2415, 74865, -2919735, 137227545, -7547514975, 475493443425]
PolyCol9 [1, 1, -8, 136, -3536, 123760, -5445440, 288608320, -17893715840, 1270453824640]