A265314 Triangle read by rows, the numerators of the Bell transform of B(n,1) where B(n,x) are the Bernoulli polynomials.

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.

Links

Table of n, a(n) for n=0..65.

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

Adjacent sequences: A265311 A265312 A265313 * A265315 A265316 A265317

Keyword

sign,tabl,frac

Author

Peter Luschny, Jan 22 2016

Status

approved