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A265604
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Triangle read by rows: The inverse Bell transform of the quartic factorial numbers (A007696).
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7
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1, 0, 1, 0, 1, 1, 0, -2, 3, 1, 0, 10, -5, 6, 1, 0, -80, 30, -5, 10, 1, 0, 880, -290, 45, 5, 15, 1, 0, -12320, 3780, -560, 35, 35, 21, 1, 0, 209440, -61460, 8820, -735, 0, 98, 28, 1, 0, -4188800, 1192800, -167300, 14700, -735, 0, 210, 36, 1
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OFFSET
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0,8
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LINKS
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EXAMPLE
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[ 1]
[ 0, 1]
[ 0, 1, 1]
[ 0, -2, 3, 1]
[ 0, 10, -5, 6, 1]
[ 0, -80, 30, -5, 10, 1]
[ 0, 880, -290, 45, 5, 15, 1]
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PROG
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(Sage) # uses[bell_transform from A264428]
def inverse_bell_matrix(generator, dim):
G = [generator(k) for k in srange(dim)]
row = lambda n: bell_transform(n, G)
M = matrix(ZZ, [row(n)+[0]*(dim-n-1) for n in srange(dim)]).inverse()
return matrix(ZZ, dim, lambda n, k: (-1)^(n-k)*M[n, k])
multifact_4_1 = lambda n: prod(4*k + 1 for k in (0..n-1))
print(inverse_bell_matrix(multifact_4_1, 8))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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