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Schroeder

['A122538', 'A033877', 'A080245', 'A080247', 'A106579']

Schroeder Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, 2, 1]
Row3 [0, 6, 4, 1]
Row4 [0, 22, 16, 6, 1]
Row5 [0, 90, 68, 30, 8, 1]
Row6 [0, 394, 304, 146, 48, 10, 1]
Row7 [0, 1806, 1412, 714, 264, 70, 12, 1]
Row8 [0, 8558, 6752, 3534, 1408, 430, 96, 14, 1]
Row9 [0, 41586, 33028, 17718, 7432, 2490, 652, 126, 16, 1]

Schroeder Triangles

Flat Seq
Triangle [[1], [0, 1], [0, 2, 1], [0, 6, 4, 1], [0, 22, 16, 6, 1], [0, 90, 68, 30, 8, 1], [0, 394, 304, 146, 48, 10, 1], [0, 1806, 1412, 714, 264, 70, 12, 1], [0, 8558, 6752, 3534, 1408, 430, 96, 14, 1], [0, 41586, 33028, 17718, 7432, 2490, 652, 126, 16, 1]]
RevTabl [[1], [1, 0], [1, 2, 0], [1, 4, 6, 0], [1, 6, 16, 22, 0], [1, 8, 30, 68, 90, 0], [1, 10, 48, 146, 304, 394, 0], [1, 12, 70, 264, 714, 1412, 1806, 0], [1, 14, 96, 430, 1408, 3534, 6752, 8558, 0], [1, 16, 126, 652, 2490, 7432, 17718, 33028, 41586, 0]]
AntiDiag [[1], [0], [0, 1], [0, 2], [0, 6, 1], [0, 22, 4], [0, 90, 16, 1], [0, 394, 68, 6], [0, 1806, 304, 30, 1], [0, 8558, 1412, 146, 8]]
AccTabl [[1], [0, 1], [0, 2, 3], [0, 6, 10, 11], [0, 22, 38, 44, 45], [0, 90, 158, 188, 196, 197], [0, 394, 698, 844, 892, 902, 903], [0, 1806, 3218, 3932, 4196, 4266, 4278, 4279], [0, 8558, 15310, 18844, 20252, 20682, 20778, 20792, 20793], [0, 41586, 74614, 92332, 99764, 102254, 102906, 103032, 103048, 103049]]
RevAccTabl [[1], [1, 0], [3, 2, 0], [11, 10, 6, 0], [45, 44, 38, 22, 0], [197, 196, 188, 158, 90, 0], [903, 902, 892, 844, 698, 394, 0], [4279, 4278, 4266, 4196, 3932, 3218, 1806, 0], [20793, 20792, 20778, 20682, 20252, 18844, 15310, 8558, 0], [103049, 103048, 103032, 102906, 102254, 99764, 92332, 74614, 41586, 0]]
AccRevTabl [[1], [1, 1], [1, 3, 3], [1, 5, 11, 11], [1, 7, 23, 45, 45], [1, 9, 39, 107, 197, 197], [1, 11, 59, 205, 509, 903, 903], [1, 13, 83, 347, 1061, 2473, 4279, 4279], [1, 15, 111, 541, 1949, 5483, 12235, 20793, 20793], [1, 17, 143, 795, 3285, 10717, 28435, 61463, 103049, 103049]]
DiffxTabl [[1], [0, 2], [0, 4, 3], [0, 12, 12, 4], [0, 44, 48, 24, 5], [0, 180, 204, 120, 40, 6], [0, 788, 912, 584, 240, 60, 7], [0, 3612, 4236, 2856, 1320, 420, 84, 8], [0, 17116, 20256, 14136, 7040, 2580, 672, 112, 9], [0, 83172, 99084, 70872, 37160, 14940, 4564, 1008, 144, 10]]

Schroeder Row sums

Trait Seq
RowSum [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049]
EvenSum [1, 0, 1, 4, 17, 76, 353, 1688, 8257, 41128]
OddSum [0, 1, 2, 7, 28, 121, 550, 2591, 12536, 61921]
AltSum [1, -1, -1, -3, -11, -45, -197, -903, -4279, -20793]
AbsSum [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049]
AccSum [1, 1, 5, 27, 149, 829, 4633, 25975, 146009, 822585]
AccRevSum [1, 2, 7, 28, 121, 550, 2591, 12536, 61921, 310954]
DiagSum [1, 0, 1, 2, 7, 26, 107, 468, 2141, 10124]

Schroeder Transforms

Trans Seq
RowLcm [1, 1, 2, 12, 528, 6120, 65577360, 2384317320, 307331984910720, 10705170228466855130640]
RowGcd [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]
RowMax [1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586]
CentralE [1, 2, 16, 146, 1408]
CentralO [0, 6, 68, 714, 7432]
ColMiddle [1, 0, 2, 6, 16, 68, 146, 714, 1408, 7432]
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, 5, 31, 209, 1471, 10625, 78079, 580865, 4361215]
InvBinConv [1, 1, -3, 7, -15, 31, -63, 127, -255, 511]
TransSqrs [0, 1, 6, 31, 156, 785, 3978, 20335, 104856, 545073]
TransNat0 [0, 1, 4, 17, 76, 353, 1688, 8257, 41128, 207905]
TransNat1 [1, 2, 7, 28, 121, 550, 2591, 12536, 61921, 310954]
PosHalf [1, 1, 5, 33, 253, 2121, 18853, 174609, 1667021, 16290969]
NegHalf [1, 1, -3, 17, -123, 1001, -8739, 79969, -756939, 7349657]

Schroeder Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]
DiagRow2 [0, 6, 16, 30, 48, 70, 96, 126, 160, 198]
DiagRow3 [0, 22, 68, 146, 264, 430, 652, 938, 1296, 1734]
DiagRow4 [0, 90, 304, 714, 1408, 2490, 4080, 6314, 9344, 13338]
DiagRow5 [0, 394, 1412, 3534, 7432, 14002, 24396, 40054, 62736, 94554]
DiagRow6 [0, 1806, 6752, 17718, 39152, 77550, 142000, 244790, 402080, 634638]
DiagRow7 [0, 8558, 33028, 89898, 206600, 426150, 812940, 1459810, 2496528, 4099806]
DiagRow8 [0, 41586, 164512, 461010, 1093760, 2332850, 4605600, 8561938, 15158272, 25763058]
DiagRow9 [0, 206098, 831620, 2386390, 5813000, 12751450, 25918988, 49639198, 90560528, 158611106]

Schroeder Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098]
DiagCol2 [1, 4, 16, 68, 304, 1412, 6752, 33028, 164512, 831620]
DiagCol3 [1, 6, 30, 146, 714, 3534, 17718, 89898, 461010, 2386390]
DiagCol4 [1, 8, 48, 264, 1408, 7432, 39152, 206600, 1093760, 5813000]
DiagCol5 [1, 10, 70, 430, 2490, 14002, 77550, 426150, 2332850, 12751450]
DiagCol6 [1, 12, 96, 652, 4080, 24396, 142000, 812940, 4605600, 25918988]
DiagCol7 [1, 14, 126, 938, 6314, 40054, 244790, 1459810, 8561938, 49639198]
DiagCol8 [1, 16, 160, 1296, 9344, 62736, 402080, 2496528, 15158272, 90560528]
DiagCol9 [1, 18, 198, 1734, 13338, 94554, 634638, 4099806, 25763058, 158611106]

Schroeder 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, 3, 8, 15, 24, 35, 48, 63, 80, 99]
PolyRow3 [0, 11, 36, 81, 152, 255, 396, 581, 816, 1107]
PolyRow4 [0, 45, 172, 453, 984, 1885, 3300, 5397, 8368, 12429]
PolyRow5 [0, 197, 852, 2583, 6440, 14025, 27612, 50267, 85968, 139725]
PolyRow6 [0, 903, 4324, 14907, 42408, 104695, 231468, 468699, 883792, 1571463]
PolyRow7 [0, 4279, 22332, 86733, 280312, 782955, 1942164, 4372417, 9088368, 17676927]
PolyRow8 [0, 20793, 116876, 507561, 1857336, 5861465, 16303908, 40799241, 93470576, 198855801]
PolyRow9 [0, 103049, 618084, 2982987, 12326792, 43909005, 136902924, 380744399, 961364112, 2237080977]

Schroeder Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049]
PolyCol2 [1, 2, 8, 36, 172, 852, 4324, 22332, 116876, 618084]
PolyCol3 [1, 3, 15, 81, 453, 2583, 14907, 86733, 507561, 2982987]
PolyCol4 [1, 4, 24, 152, 984, 6440, 42408, 280312, 1857336, 12326792]
PolyCol5 [1, 5, 35, 255, 1885, 14025, 104695, 782955, 5861465, 43909005]
PolyCol6 [1, 6, 48, 396, 3300, 27612, 231468, 1942164, 16303908, 136902924]
PolyCol7 [1, 7, 63, 581, 5397, 50267, 468699, 4372417, 40799241, 380744399]
PolyCol8 [1, 8, 80, 816, 8368, 85968, 883792, 9088368, 93470576, 961364112]
PolyCol9 [1, 9, 99, 1107, 12429, 139725, 1571463, 17676927, 198855801, 2237080977]

Schroeder:Inv

[]

Schroeder:Inv Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, -2, 1]
Row3 [0, 2, -4, 1]
Row4 [0, -2, 8, -6, 1]
Row5 [0, 2, -12, 18, -8, 1]
Row6 [0, -2, 16, -38, 32, -10, 1]
Row7 [0, 2, -20, 66, -88, 50, -12, 1]
Row8 [0, -2, 24, -102, 192, -170, 72, -14, 1]
Row9 [0, 2, -28, 146, -360, 450, -292, 98, -16, 1]

Schroeder:Inv Triangles

Flat Seq
Triangle [[1], [0, 1], [0, -2, 1], [0, 2, -4, 1], [0, -2, 8, -6, 1], [0, 2, -12, 18, -8, 1], [0, -2, 16, -38, 32, -10, 1], [0, 2, -20, 66, -88, 50, -12, 1], [0, -2, 24, -102, 192, -170, 72, -14, 1], [0, 2, -28, 146, -360, 450, -292, 98, -16, 1]]
RevTabl [[1], [1, 0], [1, -2, 0], [1, -4, 2, 0], [1, -6, 8, -2, 0], [1, -8, 18, -12, 2, 0], [1, -10, 32, -38, 16, -2, 0], [1, -12, 50, -88, 66, -20, 2, 0], [1, -14, 72, -170, 192, -102, 24, -2, 0], [1, -16, 98, -292, 450, -360, 146, -28, 2, 0]]
AntiDiag [[1], [0], [0, 1], [0, -2], [0, 2, 1], [0, -2, -4], [0, 2, 8, 1], [0, -2, -12, -6], [0, 2, 16, 18, 1], [0, -2, -20, -38, -8]]
AccTabl [[1], [0, 1], [0, -2, -1], [0, 2, -2, -1], [0, -2, 6, 0, 1], [0, 2, -10, 8, 0, 1], [0, -2, 14, -24, 8, -2, -1], [0, 2, -18, 48, -40, 10, -2, -1], [0, -2, 22, -80, 112, -58, 14, 0, 1], [0, 2, -26, 120, -240, 210, -82, 16, 0, 1]]
RevAccTabl [[1], [1, 0], [-1, -2, 0], [-1, -2, 2, 0], [1, 0, 6, -2, 0], [1, 0, 8, -10, 2, 0], [-1, -2, 8, -24, 14, -2, 0], [-1, -2, 10, -40, 48, -18, 2, 0], [1, 0, 14, -58, 112, -80, 22, -2, 0], [1, 0, 16, -82, 210, -240, 120, -26, 2, 0]]
AccRevTabl [[1], [1, 1], [1, -1, -1], [1, -3, -1, -1], [1, -5, 3, 1, 1], [1, -7, 11, -1, 1, 1], [1, -9, 23, -15, 1, -1, -1], [1, -11, 39, -49, 17, -3, -1, -1], [1, -13, 59, -111, 81, -21, 3, 1, 1], [1, -15, 83, -209, 241, -119, 27, -1, 1, 1]]
DiffxTabl [[1], [0, 2], [0, -4, 3], [0, 4, -12, 4], [0, -4, 24, -24, 5], [0, 4, -36, 72, -40, 6], [0, -4, 48, -152, 160, -60, 7], [0, 4, -60, 264, -440, 300, -84, 8], [0, -4, 72, -408, 960, -1020, 504, -112, 9], [0, 4, -84, 584, -1800, 2700, -2044, 784, -144, 10]]

Schroeder:Inv Row sums

Trait Seq
RowSum [1, 1, -1, -1, 1, 1, -1, -1, 1, 1]
EvenSum [1, 0, 1, -4, 9, -20, 49, -120, 289, -696]
OddSum [0, 1, -2, 3, -8, 21, -50, 119, -288, 697]
AltSum [1, -1, 3, -7, 17, -41, 99, -239, 577, -1393]
AbsSum [1, 1, 3, 7, 17, 41, 99, 239, 577, 1393]
AccSum [1, 1, -3, -1, 5, 1, -7, -1, 9, 1]
AccRevSum [1, 2, -1, -4, 1, 6, -1, -8, 1, 10]
DiagSum [1, 0, 1, -2, 3, -6, 11, -20, 37, -68]

Schroeder:Inv Transforms

Trans Seq
RowLcm [1, 1, 2, 4, 24, 72, 3040, 6600, 342720, 12877200]
RowGcd [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]
RowMax [1, 1, 2, 4, 8, 18, 38, 88, 192, 450]
CentralE [1, -2, 8, -38, 192]
CentralO [0, 2, -12, 66, -360]
ColMiddle [1, 0, -2, 2, 8, -12, -38, 66, 192, -360]
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, -5, 17, 31, -111, -209, 769, 1471]
InvBinConv [1, 1, 5, 19, 81, 351, 1553, 6959, 31489, 143551]
TransSqrs [0, 1, 2, -5, -8, 13, 18, -25, -32, 41]
TransNat0 [0, 1, 0, -3, 0, 5, 0, -7, 0, 9]
TransNat1 [1, 2, -1, -4, 1, 6, -1, -8, 1, 10]
PosHalf [1, 1, -3, 1, 5, -7, -3, 17, -11, -23]
NegHalf [1, 1, 5, 17, 61, 217, 773, 2753, 9805, 34921]

Schroeder:Inv Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1 [0, -2, -4, -6, -8, -10, -12, -14, -16, -18]
DiagRow2 [0, 2, 8, 18, 32, 50, 72, 98, 128, 162]
DiagRow3 [0, -2, -12, -38, -88, -170, -292, -462, -688, -978]
DiagRow4 [0, 2, 16, 66, 192, 450, 912, 1666, 2816, 4482]
DiagRow5 [0, -2, -20, -102, -360, -1002, -2364, -4942, -9424, -16722]
DiagRow6 [0, 2, 24, 146, 608, 1970, 5336, 12642, 27008, 53154]
DiagRow7 [0, -2, -28, -198, -952, -3530, -10836, -28814, -68464, -148626]
DiagRow8 [0, 2, 32, 258, 1408, 5890, 20256, 59906, 157184, 374274]
DiagRow9 [0, -2, -36, -326, -1992, -9290, -35436, -115598, -332688, -864146]

Schroeder:Inv Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, -2, 2, -2, 2, -2, 2, -2, 2, -2]
DiagCol2 [1, -4, 8, -12, 16, -20, 24, -28, 32, -36]
DiagCol3 [1, -6, 18, -38, 66, -102, 146, -198, 258, -326]
DiagCol4 [1, -8, 32, -88, 192, -360, 608, -952, 1408, -1992]
DiagCol5 [1, -10, 50, -170, 450, -1002, 1970, -3530, 5890, -9290]
DiagCol6 [1, -12, 72, -292, 912, -2364, 5336, -10836, 20256, -35436]
DiagCol7 [1, -14, 98, -462, 1666, -4942, 12642, -28814, 59906, -115598]
DiagCol8 [1, -16, 128, -688, 2816, -9424, 27008, -68464, 157184, -332688]
DiagCol9 [1, -18, 162, -978, 4482, -16722, 53154, -148626, 374274, -864146]

Schroeder: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, -1, 0, 3, 8, 15, 24, 35, 48, 63]
PolyRow3 [0, -1, -4, -3, 8, 35, 84, 161, 272, 423]
PolyRow4 [0, 1, -4, -15, -8, 65, 276, 721, 1520, 2817]
PolyRow5 [0, 1, 4, -21, -56, 85, 876, 3199, 8464, 18729]
PolyRow6 [0, -1, 12, 3, -136, 15, 2724, 14147, 47088, 124479]
PolyRow7 [0, -1, 4, 69, -184, -365, 8364, 62489, 261904, 827271]
PolyRow8 [0, 1, -20, 129, -8, -1535, 25476, 275905, 1456624, 5497857]
PolyRow9 [0, 1, -28, 51, 712, -4315, 77196, 1218007, 8101136, 36537417]

Schroeder:Inv Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, -1, -1, 1, 1, -1, -1, 1, 1]
PolyCol2 [1, 2, 0, -4, -4, 4, 12, 4, -20, -28]
PolyCol3 [1, 3, 3, -3, -15, -21, 3, 69, 129, 51]
PolyCol4 [1, 4, 8, 8, -8, -56, -136, -184, -8, 712]
PolyCol5 [1, 5, 15, 35, 65, 85, 15, -365, -1535, -4315]
PolyCol6 [1, 6, 24, 84, 276, 876, 2724, 8364, 25476, 77196]
PolyCol7 [1, 7, 35, 161, 721, 3199, 14147, 62489, 275905, 1218007]
PolyCol8 [1, 8, 48, 272, 1520, 8464, 47088, 261904, 1456624, 8101136]
PolyCol9 [1, 9, 63, 423, 2817, 18729, 124479, 827271, 5497857, 36537417]

Schroeder:Rev

[]

Schroeder:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, 2, 0]
Row3 [1, 4, 6, 0]
Row4 [1, 6, 16, 22, 0]
Row5 [1, 8, 30, 68, 90, 0]
Row6 [1, 10, 48, 146, 304, 394, 0]
Row7 [1, 12, 70, 264, 714, 1412, 1806, 0]
Row8 [1, 14, 96, 430, 1408, 3534, 6752, 8558, 0]
Row9 [1, 16, 126, 652, 2490, 7432, 17718, 33028, 41586, 0]

Schroeder:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, 2, 0], [1, 4, 6, 0], [1, 6, 16, 22, 0], [1, 8, 30, 68, 90, 0], [1, 10, 48, 146, 304, 394, 0], [1, 12, 70, 264, 714, 1412, 1806, 0], [1, 14, 96, 430, 1408, 3534, 6752, 8558, 0], [1, 16, 126, 652, 2490, 7432, 17718, 33028, 41586, 0]]
RevTabl [[1], [0, 1], [0, 2, 1], [0, 6, 4, 1], [0, 22, 16, 6, 1], [0, 90, 68, 30, 8, 1], [0, 394, 304, 146, 48, 10, 1], [0, 1806, 1412, 714, 264, 70, 12, 1], [0, 8558, 6752, 3534, 1408, 430, 96, 14, 1], [0, 41586, 33028, 17718, 7432, 2490, 652, 126, 16, 1]]
AntiDiag [[1], [1], [1, 0], [1, 2], [1, 4, 0], [1, 6, 6], [1, 8, 16, 0], [1, 10, 30, 22], [1, 12, 48, 68, 0], [1, 14, 70, 146, 90]]
AccTabl [[1], [1, 1], [1, 3, 3], [1, 5, 11, 11], [1, 7, 23, 45, 45], [1, 9, 39, 107, 197, 197], [1, 11, 59, 205, 509, 903, 903], [1, 13, 83, 347, 1061, 2473, 4279, 4279], [1, 15, 111, 541, 1949, 5483, 12235, 20793, 20793], [1, 17, 143, 795, 3285, 10717, 28435, 61463, 103049, 103049]]
RevAccTabl [[1], [1, 1], [3, 3, 1], [11, 11, 5, 1], [45, 45, 23, 7, 1], [197, 197, 107, 39, 9, 1], [903, 903, 509, 205, 59, 11, 1], [4279, 4279, 2473, 1061, 347, 83, 13, 1], [20793, 20793, 12235, 5483, 1949, 541, 111, 15, 1], [103049, 103049, 61463, 28435, 10717, 3285, 795, 143, 17, 1]]
AccRevTabl [[1], [0, 1], [0, 2, 3], [0, 6, 10, 11], [0, 22, 38, 44, 45], [0, 90, 158, 188, 196, 197], [0, 394, 698, 844, 892, 902, 903], [0, 1806, 3218, 3932, 4196, 4266, 4278, 4279], [0, 8558, 15310, 18844, 20252, 20682, 20778, 20792, 20793], [0, 41586, 74614, 92332, 99764, 102254, 102906, 103032, 103048, 103049]]
DiffxTabl [[1], [1, 0], [1, 4, 0], [1, 8, 18, 0], [1, 12, 48, 88, 0], [1, 16, 90, 272, 450, 0], [1, 20, 144, 584, 1520, 2364, 0], [1, 24, 210, 1056, 3570, 8472, 12642, 0], [1, 28, 288, 1720, 7040, 21204, 47264, 68464, 0], [1, 32, 378, 2608, 12450, 44592, 124026, 264224, 374274, 0]]

Schroeder:Rev Row sums

Trait Seq
RowSum [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049]
EvenSum [1, 1, 1, 7, 17, 121, 353, 2591, 8257, 61921]
OddSum [0, 0, 2, 4, 28, 76, 550, 1688, 12536, 41128]
AltSum [1, 1, -1, 3, -11, 45, -197, 903, -4279, 20793]
AbsSum [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049]
AccSum [1, 2, 7, 28, 121, 550, 2591, 12536, 61921, 310954]
AccRevSum [1, 1, 5, 27, 149, 829, 4633, 25975, 146009, 822585]
DiagSum [1, 1, 1, 3, 5, 13, 25, 63, 129, 321]

Schroeder:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 12, 528, 6120, 65577360, 2384317320, 307331984910720, 10705170228466855130640]
RowGcd [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]
RowMax [1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586]
CentralE [1, 2, 16, 146, 1408]
CentralO [1, 4, 30, 264, 2490]
ColMiddle [1, 1, 2, 4, 16, 30, 146, 264, 1408, 2490]
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, 5, 31, 209, 1471, 10625, 78079, 580865, 4361215]
InvBinConv [1, -1, -3, -7, -15, -31, -63, -127, -255, -511]
TransSqrs [0, 0, 2, 28, 268, 2180, 16230, 114408, 777560, 5149752]
TransNat0 [0, 0, 2, 16, 104, 632, 3730, 21696, 125216, 719536]
TransNat1 [1, 1, 5, 27, 149, 829, 4633, 25975, 146009, 822585]
PosHalf [1, 2, 8, 36, 172, 852, 4324, 22332, 116876, 618084]
NegHalf [1, -2, 0, -4, -12, -52, -228, -1052, -5004, -24388]

Schroeder:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098]
DiagRow2 [1, 4, 16, 68, 304, 1412, 6752, 33028, 164512, 831620]
DiagRow3 [1, 6, 30, 146, 714, 3534, 17718, 89898, 461010, 2386390]
DiagRow4 [1, 8, 48, 264, 1408, 7432, 39152, 206600, 1093760, 5813000]
DiagRow5 [1, 10, 70, 430, 2490, 14002, 77550, 426150, 2332850, 12751450]
DiagRow6 [1, 12, 96, 652, 4080, 24396, 142000, 812940, 4605600, 25918988]
DiagRow7 [1, 14, 126, 938, 6314, 40054, 244790, 1459810, 8561938, 49639198]
DiagRow8 [1, 16, 160, 1296, 9344, 62736, 402080, 2496528, 15158272, 90560528]
DiagRow9 [1, 18, 198, 1734, 13338, 94554, 634638, 4099806, 25763058, 158611106]

Schroeder:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]
DiagCol2 [0, 6, 16, 30, 48, 70, 96, 126, 160, 198]
DiagCol3 [0, 22, 68, 146, 264, 430, 652, 938, 1296, 1734]
DiagCol4 [0, 90, 304, 714, 1408, 2490, 4080, 6314, 9344, 13338]
DiagCol5 [0, 394, 1412, 3534, 7432, 14002, 24396, 40054, 62736, 94554]
DiagCol6 [0, 1806, 6752, 17718, 39152, 77550, 142000, 244790, 402080, 634638]
DiagCol7 [0, 8558, 33028, 89898, 206600, 426150, 812940, 1459810, 2496528, 4099806]
DiagCol8 [0, 41586, 164512, 461010, 1093760, 2332850, 4605600, 8561938, 15158272, 25763058]
DiagCol9 [0, 206098, 831620, 2386390, 5813000, 12751450, 25918988, 49639198, 90560528, 158611106]

Schroeder: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, 3, 5, 7, 9, 11, 13, 15, 17, 19]
PolyRow3 [1, 11, 33, 67, 113, 171, 241, 323, 417, 523]
PolyRow4 [1, 45, 253, 757, 1689, 3181, 5365, 8373, 12337, 17389]
PolyRow5 [1, 197, 2121, 9421, 27905, 65541, 132457, 240941, 405441, 642565]
PolyRow6 [1, 903, 18853, 124771, 491433, 1440751, 3491053, 7404363, 14233681, 25370263]
PolyRow7 [1, 4279, 174609, 1725319, 9044113, 33112311, 96225409, 238013959, 522764769, 1048042423]
PolyRow8 [1, 20793, 1667021, 24623881, 171878841, 786073721, 2740115173, 7905175881, 19839218801, 44739176761]
PolyRow9 [1, 103049, 16290969, 360020857, 3347375393, 19126553481, 79982051929, 269150615609, 771860781057, 1957984585993]

Schroeder:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049]
PolyCol2 [1, 1, 5, 33, 253, 2121, 18853, 174609, 1667021, 16290969]
PolyCol3 [1, 1, 7, 67, 757, 9421, 124771, 1725319, 24623881, 360020857]
PolyCol4 [1, 1, 9, 113, 1689, 27905, 491433, 9044113, 171878841, 3347375393]
PolyCol5 [1, 1, 11, 171, 3181, 65541, 1440751, 33112311, 786073721, 19126553481]
PolyCol6 [1, 1, 13, 241, 5365, 132457, 3491053, 96225409, 2740115173, 79982051929]
PolyCol7 [1, 1, 15, 323, 8373, 240941, 7404363, 238013959, 7905175881, 269150615609]
PolyCol8 [1, 1, 17, 417, 12337, 405441, 14233681, 522764769, 19839218801, 771860781057]
PolyCol9 [1, 1, 19, 523, 17389, 642565, 25370263, 1048042423, 44739176761, 1957984585993]

Schroeder:Inv:Rev

[]

Schroeder:Inv:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [1, -2, 0]
Row3 [1, -4, 2, 0]
Row4 [1, -6, 8, -2, 0]
Row5 [1, -8, 18, -12, 2, 0]
Row6 [1, -10, 32, -38, 16, -2, 0]
Row7 [1, -12, 50, -88, 66, -20, 2, 0]
Row8 [1, -14, 72, -170, 192, -102, 24, -2, 0]
Row9 [1, -16, 98, -292, 450, -360, 146, -28, 2, 0]

Schroeder:Inv:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [1, -2, 0], [1, -4, 2, 0], [1, -6, 8, -2, 0], [1, -8, 18, -12, 2, 0], [1, -10, 32, -38, 16, -2, 0], [1, -12, 50, -88, 66, -20, 2, 0], [1, -14, 72, -170, 192, -102, 24, -2, 0], [1, -16, 98, -292, 450, -360, 146, -28, 2, 0]]
RevTabl [[1], [0, 1], [0, -2, 1], [0, 2, -4, 1], [0, -2, 8, -6, 1], [0, 2, -12, 18, -8, 1], [0, -2, 16, -38, 32, -10, 1], [0, 2, -20, 66, -88, 50, -12, 1], [0, -2, 24, -102, 192, -170, 72, -14, 1], [0, 2, -28, 146, -360, 450, -292, 98, -16, 1]]
AntiDiag [[1], [1], [1, 0], [1, -2], [1, -4, 0], [1, -6, 2], [1, -8, 8, 0], [1, -10, 18, -2], [1, -12, 32, -12, 0], [1, -14, 50, -38, 2]]
AccTabl [[1], [1, 1], [1, -1, -1], [1, -3, -1, -1], [1, -5, 3, 1, 1], [1, -7, 11, -1, 1, 1], [1, -9, 23, -15, 1, -1, -1], [1, -11, 39, -49, 17, -3, -1, -1], [1, -13, 59, -111, 81, -21, 3, 1, 1], [1, -15, 83, -209, 241, -119, 27, -1, 1, 1]]
RevAccTabl [[1], [1, 1], [-1, -1, 1], [-1, -1, -3, 1], [1, 1, 3, -5, 1], [1, 1, -1, 11, -7, 1], [-1, -1, 1, -15, 23, -9, 1], [-1, -1, -3, 17, -49, 39, -11, 1], [1, 1, 3, -21, 81, -111, 59, -13, 1], [1, 1, -1, 27, -119, 241, -209, 83, -15, 1]]
AccRevTabl [[1], [0, 1], [0, -2, -1], [0, 2, -2, -1], [0, -2, 6, 0, 1], [0, 2, -10, 8, 0, 1], [0, -2, 14, -24, 8, -2, -1], [0, 2, -18, 48, -40, 10, -2, -1], [0, -2, 22, -80, 112, -58, 14, 0, 1], [0, 2, -26, 120, -240, 210, -82, 16, 0, 1]]
DiffxTabl [[1], [1, 0], [1, -4, 0], [1, -8, 6, 0], [1, -12, 24, -8, 0], [1, -16, 54, -48, 10, 0], [1, -20, 96, -152, 80, -12, 0], [1, -24, 150, -352, 330, -120, 14, 0], [1, -28, 216, -680, 960, -612, 168, -16, 0], [1, -32, 294, -1168, 2250, -2160, 1022, -224, 18, 0]]

Schroeder:Inv:Rev Row sums

Trait Seq
RowSum [1, 1, -1, -1, 1, 1, -1, -1, 1, 1]
EvenSum [1, 1, 1, 3, 9, 21, 49, 119, 289, 697]
OddSum [0, 0, -2, -4, -8, -20, -50, -120, -288, -696]
AltSum [1, 1, 3, 7, 17, 41, 99, 239, 577, 1393]
AbsSum [1, 1, 3, 7, 17, 41, 99, 239, 577, 1393]
AccSum [1, 2, -1, -4, 1, 6, -1, -8, 1, 10]
AccRevSum [1, 1, -3, -1, 5, 1, -7, -1, 9, 1]
DiagSum [1, 1, 1, -1, -3, -3, 1, 7, 9, 1]

Schroeder:Inv:Rev Transforms

Trans Seq
RowLcm [1, 1, 2, 4, 24, 72, 3040, 6600, 342720, 12877200]
RowGcd [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]
RowMax [1, 1, 2, 4, 8, 18, 38, 88, 192, 450]
CentralE [1, -2, 8, -38, 192]
CentralO [1, -4, 18, -88, 450]
ColMiddle [1, 1, -2, -4, 8, 18, -38, -88, 192, 450]
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, -5, 17, 31, -111, -209, 769, 1471]
InvBinConv [1, -1, 5, -19, 81, -351, 1553, -6959, 31489, -143551]
TransSqrs [0, 0, -2, 4, 8, -12, -18, 24, 32, -40]
TransNat0 [0, 0, -2, 0, 4, 0, -6, 0, 8, 0]
TransNat1 [1, 1, -3, -1, 5, 1, -7, -1, 9, 1]
PosHalf [1, 2, 0, -4, -4, 4, 12, 4, -20, -28]
NegHalf [1, -2, 8, -28, 100, -356, 1268, -4516, 16084, -57284]

Schroeder:Inv:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, -2, 2, -2, 2, -2, 2, -2, 2, -2]
DiagRow2 [1, -4, 8, -12, 16, -20, 24, -28, 32, -36]
DiagRow3 [1, -6, 18, -38, 66, -102, 146, -198, 258, -326]
DiagRow4 [1, -8, 32, -88, 192, -360, 608, -952, 1408, -1992]
DiagRow5 [1, -10, 50, -170, 450, -1002, 1970, -3530, 5890, -9290]
DiagRow6 [1, -12, 72, -292, 912, -2364, 5336, -10836, 20256, -35436]
DiagRow7 [1, -14, 98, -462, 1666, -4942, 12642, -28814, 59906, -115598]
DiagRow8 [1, -16, 128, -688, 2816, -9424, 27008, -68464, 157184, -332688]
DiagRow9 [1, -18, 162, -978, 4482, -16722, 53154, -148626, 374274, -864146]

Schroeder:Inv:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1 [0, -2, -4, -6, -8, -10, -12, -14, -16, -18]
DiagCol2 [0, 2, 8, 18, 32, 50, 72, 98, 128, 162]
DiagCol3 [0, -2, -12, -38, -88, -170, -292, -462, -688, -978]
DiagCol4 [0, 2, 16, 66, 192, 450, 912, 1666, 2816, 4482]
DiagCol5 [0, -2, -20, -102, -360, -1002, -2364, -4942, -9424, -16722]
DiagCol6 [0, 2, 24, 146, 608, 1970, 5336, 12642, 27008, 53154]
DiagCol7 [0, -2, -28, -198, -952, -3530, -10836, -28814, -68464, -148626]
DiagCol8 [0, 2, 32, 258, 1408, 5890, 20256, 59906, 157184, 374274]
DiagCol9 [0, -2, -36, -326, -1992, -9290, -35436, -115598, -332688, -864146]

Schroeder: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, -1, -3, -5, -7, -9, -11, -13, -15, -17]
PolyRow3 [1, -1, 1, 7, 17, 31, 49, 71, 97, 127]
PolyRow4 [1, 1, 5, 1, -23, -79, -179, -335, -559, -863]
PolyRow5 [1, 1, -7, -23, 1, 161, 601, 1513, 3137, 5761]
PolyRow6 [1, -1, -3, 43, 89, -249, -1931, -6733, -17487, -38321]
PolyRow7 [1, -1, 17, -17, -271, 191, 6049, 29807, 97313, 254719]
PolyRow8 [1, 1, -11, -95, 457, 481, -18659, -131711, -541295, -1692863]
PolyRow9 [1, 1, -23, 241, -287, -2879, 57001, 581617, 3010561, 11250433]

Schroeder:Inv:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1 [1, 1, -1, -1, 1, 1, -1, -1, 1, 1]
PolyCol2 [1, 1, -3, 1, 5, -7, -3, 17, -11, -23]
PolyCol3 [1, 1, -5, 7, 1, -23, 43, -17, -95, 241]
PolyCol4 [1, 1, -7, 17, -23, 1, 89, -271, 457, -287]
PolyCol5 [1, 1, -9, 31, -79, 161, -249, 191, 481, -2879]
PolyCol6 [1, 1, -11, 49, -179, 601, -1931, 6049, -18659, 57001]
PolyCol7 [1, 1, -13, 71, -335, 1513, -6733, 29807, -131711, 581617]
PolyCol8 [1, 1, -15, 97, -559, 3137, -17487, 97313, -541295, 3010561]
PolyCol9 [1, 1, -17, 127, -863, 5761, -38321, 254719, -1692863, 11250433]