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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 (list; table; graph; refs; listen; history; text; internal format)
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 * A307791 A307766 A025443

Adjacent sequences:  A265311 A265312 A265313 * A265315 A265316 A265317

KEYWORD

sign,tabl,frac

AUTHOR

Peter Luschny, Jan 22 2016

STATUS

approved

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Last modified November 22 06:15 EST 2019. Contains 329389 sequences. (Running on oeis4.)