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A265602
Triangle read by rows, the numerators of the Bell transform of B(2n,1) where B(n,x) are the Bernoulli polynomials.
3
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
OFFSET
0,18
COMMENTS
For the definition of the Bell transform see A264428 and the link given there.
EXAMPLE
Triangle begins:
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.
MAPLE
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:
A265602_triangle(10);
MATHEMATICA
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 (* Jean-François Alcover, Jun 27 2018, from Maple *)
CROSSREFS
Cf. A265603 for the denominators, A265314 and A265315 for B(n,1).
Cf. A000367 (column 1).
Sequence in context: A303144 A370451 A390489 * A185373 A244759 A194127
KEYWORD
sign,tabl,frac
AUTHOR
Peter Luschny, Jan 21 2016
STATUS
approved