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A228969 Triangle of numerators of the coefficients t(n,k) in the formula B(2n) = -sum_{k=1..n-1} t(n,k)*B(2k)*B(2n-2k), where the B() are the even-indexed Bernoulli numbers.

%I A228969 #17 Sep 12 2013 10:50:35
%S A228969 6,5,25,28,70,588,45,1050,4410,3825,22,165,924,2805,7502,91,5005,
%T A228969 63063,255255,341341,124215,24,1820,168168,12870,2730728,496860,
%U A228969 131064,17,1700,6188,413270,1657942,402220,1856740,371365
%N A228969 Triangle of numerators of the coefficients t(n,k) in the formula B(2n) = -sum_{k=1..n-1} t(n,k)*B(2k)*B(2n-2k), where the B() are the even-indexed Bernoulli numbers.
%D A228969 George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 100.
%H A228969 Jean-François Alcover, <a href="/A228969/b228969.txt">Table of n, a(n) for n = 2..105</a>
%e A228969 6/5;
%e A228969 5/7,       25/7;
%e A228969 28/85,     70/17,  588/85;
%e A228969 45/341, 1050/341, 4410/341, 3825/341;
%e A228969 ...
%t A228969 Table[(2^(2*k) - 1)/(2^(2*n) - 1)* Binomial[2*n, 2*k], {n, 2, 9}, {k, 1, n-1}] // Flatten // Numerator
%Y A228969 Cf. A228970 (denominators).
%K A228969 frac,nonn,tabl
%O A228969 2,1
%A A228969 _Jean-François Alcover_, Sep 10 2013