A265602 Triangle read by rows, the numerators of the Bell transform of B(2n,1) where B(n,x) are the Bernoulli polynomials.

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.

Links

Table of n, a(n) for n=0..54.

Example

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 (*~, from Maple *) ~~~

Crossrefs

Cf. A265603 for the denominators, A265314 and A265315 for B(n,1).

Cf. A000367 (column 1).

Sequence in context: A076810 A303144 A370451 * A185373 A244759 A194127

Adjacent sequences: A265599 A265600 A265601 * A265603 A265604 A265605

Keyword

sign,tabl,frac

Author

Peter Luschny, Jan 21 2016

Status

approved