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%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
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