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%I A265603 #19 Jun 27 2018 02:47:16
%S A265603 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 A265603 1,2730,495,360,72,4,2,1,1,6,900900,5940,432,2,30,3,1,1,510,15015,
%U A265603 1351350,990,80,6,10,1,1,1,798,5105100,360360,154440,1056,80,12,2,2,1
%N A265603 Triangle read by rows, the denominators of the Bell transform of B(2n,1) where B(n,x) are the Bernoulli polynomials.
%C A265603 For the definition of the Bell transform see A264428 and the link given there.
%e A265603 1,
%e A265603 1,    1,
%e A265603 1,    6,      1,
%e A265603 1,   30,      2,       1,
%e A265603 1,   42,     20,       1,   1,
%e A265603 1,   30,     63,      12,   3,  1,
%e A265603 1,   66,   1260,     504,  12,  2,  1,
%e A265603 1, 2730,    495,     360,  72,  4,  2,  1,
%e A265603 1,    6, 900900,    5940, 432,  2, 30,  3, 1,
%e A265603 1,  510,  15015, 1351350, 990, 80,  6, 10, 1, 1.
%p A265603 A265603_triangle := proc(n) local B,C,k;
%p A265603 B := BellMatrix(x -> bernoulli(2*x,1), n); # see A264428
%p A265603 for k from 1 to n do
%p A265603    C := LinearAlgebra:-Row(B,k):
%p A265603    print(seq(denom(C[j]), j=1..k))
%p A265603 od end:
%p A265603 A265603_triangle(10);
%t A265603 BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
%t A265603 rows = 12;
%t A265603 B = BellMatrix[BernoulliB[2#, 1]&, rows];
%t A265603 Table[B[[n, k]] // Denominator, {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 27 2018, from Maple *)
%Y A265603 Cf. A265602 for the numerators, A265314 and A265315 for B(n,1).
%Y A265603 Cf. A002445 (column 1).
%K A265603 nonn,tabl,frac
%O A265603 0,5
%A A265603 _Peter Luschny_, Jan 21 2016

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