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Bessel2.py
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Bessel2.py
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from functools import cache
from _tabltypes import MakeTriangle
"""Bessel2 triangle.
[0] 1
[1] 1, 0
[2] 1, 0, 1
[3] 1, 0, 3, 0
[4] 1, 0, 6, 0, 3
[5] 1, 0, 10, 0, 15, 0
[6] 1, 0, 15, 0, 45, 0, 15
[7] 1, 0, 21, 0, 105, 0, 105, 0
[8] 1, 0, 28, 0, 210, 0, 420, 0, 105
[9] 1, 0, 36, 0, 378, 0, 1260, 0, 945, 0
"""
@cache
def bessel2(n: int) -> list[int]:
if n == 0:
return [1]
if n == 1:
return [1, 0]
row = bessel2(n - 1) + [0]
row[n] = 0 if n % 2 else row[n - 2]
for k in range(2, n, 2):
row[k] = (n * row[k]) // (n - k)
return row
@MakeTriangle(
bessel2,
"Bessel2",
["A359760", "A073278", "A066325", "A099174", "A111924", "A144299", "A104556"],
False,
)
def Bessel2(n: int, k: int) -> int:
return bessel2(n)[k]
if __name__ == "__main__":
from _tabltest import TablTest
TablTest(Bessel2)