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A265314
Triangle read by rows, the numerators of the Bell transform of B(n,1) where B(n,x) are the Bernoulli polynomials.
3
1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 0, 17, 3, 1, 0, -1, 5, 65, 5, 1, 0, 0, 7, 55, 175, 15, 1, 0, 1, -7, 2023, 245, 385, 21, 1, 0, 0, -38, 49, 34181, 595, 371, 14, 1, 0, -1, 3, -14351, 973, 56567, 525, 217, 18, 1, 0, 0, 99, -19, 10637, 13601, 208859, 2415, 355, 45, 1
OFFSET
0,9
COMMENTS
For the definition of the Bell transform see A264428 and the link given there.
EXAMPLE
1,
0, 1,
0, 1, 1,
0, 1, 3, 1,
0, 0, 17, 3, 1,
0, -1, 5, 65, 5, 1,
0, 0, 7, 55, 175, 15, 1,
0, 1, -7, 2023, 245, 385, 21, 1,
0, 0, -38, 49, 34181, 595, 371, 14, 1,
0, -1, 3, -14351, 973, 56567, 525, 217, 18, 1.
MAPLE
A265314_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(numer(C[j]), j=1..k))
od end:
A265314_triangle(10);
MATHEMATICA
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]] // Numerator, {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 26 2018, from Maple *)
CROSSREFS
Cf. A265315 for the denominators, A265602 and A265603 for B(2n,1).
Cf. A027641 and A164555 (column 1).
Sequence in context: A264429 A324163 A127537 * A364207 A307791 A307766
KEYWORD
sign,tabl,frac
AUTHOR
Peter Luschny, Jan 22 2016
STATUS
approved