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A265605
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Triangle read by rows: The inverse Bell transform of the triple factorial numbers (A007559).
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6
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1, 0, 1, 0, 1, 1, 0, -1, 3, 1, 0, 3, -1, 6, 1, 0, -15, 5, 5, 10, 1, 0, 105, -35, 0, 25, 15, 1, 0, -945, 315, -35, 0, 70, 21, 1, 0, 10395, -3465, 490, -35, 70, 154, 28, 1, 0, -135135, 45045, -6895, 630, -105, 378, 294, 36, 1
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OFFSET
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0,9
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LINKS
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EXAMPLE
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[ 1]
[ 0, 1]
[ 0, 1, 1]
[ 0, -1, 3, 1]
[ 0, 3, -1, 6, 1]
[ 0, -15, 5, 5, 10, 1]
[ 0, 105, -35, 0, 25, 15, 1]
[ 0, -945, 315, -35, 0, 70, 21, 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_3_1 = lambda n: prod(3*k + 1 for k in (0..n-1))
print(inverse_bell_matrix(multifact_3_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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