A265315 - OEIS

%I #18 Jun 26 2018 04:54:12

%S 1,1,1,1,2,1,1,6,2,1,1,1,12,1,1,1,30,6,12,1,1,1,1,90,8,12,2,1,1,42,20,

%T 360,8,12,2,1,1,1,315,45,720,6,6,1,1,1,30,7,3780,20,240,2,2,1,1,1,1,

%U 350,7,756,32,240,4,2,2,1,1,66,12,6300,1512,6048,96,240,4,1,2,1

%N Triangle read by rows, the denominators 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 1,  1,

%e 1,  2,   1,

%e 1,  6,   2,    1,

%e 1,  1,  12,    1,   1,

%e 1, 30,   6,   12,   1,   1,

%e 1,  1,  90,    8,  12,   2,   1,

%e 1, 42,  20,  360,   8,  12,   2, 1,

%e 1,  1, 315,   45, 720,   6,   6, 1, 1,

%e 1, 30,   7, 3780,  20, 240,   2, 2, 1, 1,

%e 1,  1, 350,    7, 756,  32, 240, 4, 2, 2, 1.

%p A265315_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(denom(C[j]), j=1..k))

%p od end:

%p A265315_triangle(12);

%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]] // Denominator, {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 26 2018, from Maple *)

%Y Cf. A265314 for the numerators, A265602 and A265603 for B(2n,1).

%Y Cf. A027642 (column 1).

%K nonn,tabl,frac

%O 0,5

%A _Peter Luschny_, Jan 22 2016