A265314 - OEIS

%I #16 Jun 26 2018 04:54:20

%S 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,

%T -7,2023,245,385,21,1,0,0,-38,49,34181,595,371,14,1,0,-1,3,-14351,973,

%U 56567,525,217,18,1,0,0,99,-19,10637,13601,208859,2415,355,45,1

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

%C For the definition of the Bell transform see A264428 and the link given there.

%e 1,

%e 0,  1,

%e 0,  1,   1,

%e 0,  1,   3,      1,

%e 0,  0,  17,      3,     1,

%e 0, -1,   5,     65,     5,     1,

%e 0,  0,   7,     55,   175,    15,   1,

%e 0,  1,  -7,   2023,   245,   385,  21,   1,

%e 0,  0, -38,     49, 34181,   595, 371,  14,  1,

%e 0, -1,   3, -14351,   973, 56567, 525, 217, 18, 1.

%p A265314_triangle := proc(n) local B,C,k;

%p B := BellMatrix(x -> bernoulli(x,1), n); # see A264428

%p for k from 1 to n do

%p    C := LinearAlgebra:-Row(B,k):

%p    print(seq(numer(C[j]), j=1..k))

%p od end:

%p A265314_triangle(10);

%t BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

%t rows = 12;

%t B = BellMatrix[Function[x, BernoulliB[x, 1]], rows];

%t Table[B[[n, k]] // Numerator, {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 26 2018, from Maple *)

%Y Cf. A265315 for the denominators, A265602 and A265603 for B(2n,1).

%Y Cf. A027641 and A164555 (column 1).

%K sign,tabl,frac

%O 0,9

%A _Peter Luschny_, Jan 22 2016