A265602 - OEIS

%I #18 Jun 27 2018 02:47:23

%S 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,

%T -691,191,-109,11,7,7,1,0,7,-1431809,6869,-253,1,119,14,1,0,-3617,

%U 130168,-7728013,2659,-83,11,77,6,1

%N Triangle read by rows, the numerators of the Bell transform of B(2n,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,        1,        1,

%e 0,     1,       -1,        1,    1,

%e 0,    -1,        4,        1,    5,   1,

%e 0,     5,     -163,       47,    7,   5,   1,

%e 0,  -691,      191,     -109,   11,   7,   7,  1,

%e 0,     7, -1431809,     6869, -253,   1, 119, 14, 1,

%e 0, -3617,   130168, -7728013, 2659, -83,  11, 77, 6, 1.

%p A265602_triangle := proc(n) local B,C,k;

%p B := BellMatrix(x -> bernoulli(2*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 A265602_triangle(10);

%t BellMatrix[f_, 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[BernoulliB[2#, 1]&, rows];

%t Table[B[[n, k]] // Numerator, {n, 1, rows}, {k, 1, n}] // Flatten (*~, from Maple *) ~~~

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

%Y Cf. A000367 (column 1).

%K sign,tabl,frac

%O 0,18

%A _Peter Luschny_, Jan 21 2016