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A228970 Triangle of denominators 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 A228970 #25 Sep 15 2013 02:43:13
%S A228970 5,7,7,85,17,85,341,341,341,341,455,91,65,91,455,5461,5461,5461,5461,
%T A228970 5461,5461,4369,4369,21845,257,21845,4369,4369,9709,9709,1387,9709,
%U A228970 9709,1387,9709,9709
%N A228970 Triangle of denominators 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.
%C A228970 GCD of rows (5, 7, 17, 341, 13, 5461 ...) are Zsigmondy numbers A064080. - _Paul Curtz_, Sep 13 2013
%D A228970 George Boros and Victor H. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press (2006), p. 100.
%H A228970 Jean-François Alcover, <a href="/A228970/b228970.txt">Table of n, a(n) for n = 2..105</a>
%e A228970 6/5;
%e A228970 5/7,        25/7;
%e A228970 28/85,     70/17,  588/85;
%e A228970 45/341, 1050/341, 4410/341, 3825/341;
%e A228970 ...
%t A228970 Table[(2^(2*k) - 1)/(2^(2*n) - 1)* Binomial[2*n, 2*k], {n, 2, 9}, {k, 1, n-1}] // Flatten // Denominator
%Y A228970 Cf. A228969 (numerators), A064080 (Zsigmondy numbers).
%K A228970 frac,nonn,tabl
%O A228970 2,1
%A A228970 _Jean-François Alcover_, Sep 10 2013