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%I #19 Jun 27 2018 02:47:16
%S 1,1,1,1,6,1,1,30,2,1,1,42,20,1,1,1,30,63,12,3,1,1,66,1260,504,12,2,1,
%T 1,2730,495,360,72,4,2,1,1,6,900900,5940,432,2,30,3,1,1,510,15015,
%U 1351350,990,80,6,10,1,1,1,798,5105100,360360,154440,1056,80,12,2,2,1
%N Triangle read by rows, the denominators 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 1, 1,
%e 1, 6, 1,
%e 1, 30, 2, 1,
%e 1, 42, 20, 1, 1,
%e 1, 30, 63, 12, 3, 1,
%e 1, 66, 1260, 504, 12, 2, 1,
%e 1, 2730, 495, 360, 72, 4, 2, 1,
%e 1, 6, 900900, 5940, 432, 2, 30, 3, 1,
%e 1, 510, 15015, 1351350, 990, 80, 6, 10, 1, 1.
%p A265603_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(denom(C[j]), j=1..k))
%p od end:
%p A265603_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]] // Denominator, {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 27 2018, from Maple *)
%Y Cf. A265602 for the numerators, A265314 and A265315 for B(n,1).
%Y Cf. A002445 (column 1).
%K nonn,tabl,frac
%O 0,5
%A _Peter Luschny_, Jan 21 2016
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