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A265602
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Triangle read by rows, the numerators of the Bell transform of B(2n,1) where B(n,x) are the Bernoulli polynomials.
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3
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1, 0, 1, 0, 1, 1, 0, -1, 1, 1, 0, 1, -1, 1, 1, 0, -1, 4, 1, 5, 1, 0, 5, -163, 47, 7, 5, 1, 0, -691, 191, -109, 11, 7, 7, 1, 0, 7, -1431809, 6869, -253, 1, 119, 14, 1, 0, -3617, 130168, -7728013, 2659, -83, 11, 77, 6, 1
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listen;
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text;
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OFFSET
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0,18
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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,
0, 1,
0, 1, 1,
0, -1, 1, 1,
0, 1, -1, 1, 1,
0, -1, 4, 1, 5, 1,
0, 5, -163, 47, 7, 5, 1,
0, -691, 191, -109, 11, 7, 7, 1,
0, 7, -1431809, 6869, -253, 1, 119, 14, 1,
0, -3617, 130168, -7728013, 2659, -83, 11, 77, 6, 1.
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MAPLE
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A265602_triangle := proc(n) local B, C, k;
B := BellMatrix(x -> bernoulli(2*x, 1), n); # see A264428
for k from 1 to n do
C := LinearAlgebra:-Row(B, k):
print(seq(numer(C[j]), j=1..k))
od end:
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MATHEMATICA
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BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
B = BellMatrix[BernoulliB[2#, 1]&, rows];
Table[B[[n, k]] // Numerator, {n, 1, rows}, {k, 1, n}] // Flatten (*~, 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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