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A265315
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Triangle read by rows, the denominators of the Bell transform of B(n,1) where B(n,x) are the Bernoulli polynomials.
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3
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1, 1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 1, 12, 1, 1, 1, 30, 6, 12, 1, 1, 1, 1, 90, 8, 12, 2, 1, 1, 42, 20, 360, 8, 12, 2, 1, 1, 1, 315, 45, 720, 6, 6, 1, 1, 1, 30, 7, 3780, 20, 240, 2, 2, 1, 1, 1, 1, 350, 7, 756, 32, 240, 4, 2, 2, 1, 1, 66, 12, 6300, 1512, 6048, 96, 240, 4, 1, 2, 1
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OFFSET
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0,5
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COMMENTS
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For the definition of the Bell transform see A264428 and the link given there.
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LINKS
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EXAMPLE
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1,
1, 1,
1, 2, 1,
1, 6, 2, 1,
1, 1, 12, 1, 1,
1, 30, 6, 12, 1, 1,
1, 1, 90, 8, 12, 2, 1,
1, 42, 20, 360, 8, 12, 2, 1,
1, 1, 315, 45, 720, 6, 6, 1, 1,
1, 30, 7, 3780, 20, 240, 2, 2, 1, 1,
1, 1, 350, 7, 756, 32, 240, 4, 2, 2, 1.
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MAPLE
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A265315_triangle := proc(n) local B, C, k;
B := BellMatrix(x -> bernoulli(x, 1), n); # see A264428
for k from 1 to n do
C := LinearAlgebra:-Row(B, k):
print(seq(denom(C[j]), j=1..k))
od end:
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MATHEMATICA
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BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
B = BellMatrix[Function[x, BernoulliB[x, 1]], rows];
Table[B[[n, k]] // Denominator, {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 26 2018, from Maple *)
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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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