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%I #29 Aug 07 2017 10:02:37
%S 0,1,-2,1,-12,25,-1382,245,-28936,131601,-2444554,9399643,-4727281820,
%T 1000713051,-332492454406,43079206380025,-1356840503254192,
%U 1533724275728365,-157891629318320864238,723708496718865073,-1044330873985796488204
%N Numerator of 2*n*(2*n+1) B_{2*n}, where B_n are the Bernoulli numbers.
%C In 1997, Matiyasevich found the following identity;
%C (n+2) * Sum_{k=2..n-2} B_k*B_{n-k} - 2 * Sum_{k=2..n-2} binomial(n+2, k)*B_k*B_{n-k} = n*(n+1)*B_n for n > 3.
%H Seiichi Manyama, <a href="/A290533/b290533.txt">Table of n, a(n) for n = 0..314</a>
%H Y. Matiyasevich, <a href="http://logic.pdmi.ras.ru/~yumat/personaljournal/identitybernoulli/bernulli.htm">Identities with Bernoulli numbers</a>, 1997.
%H H. Pan and Z. W. Sun, <a href="http://arXiv.org/abs/math.NT/0407363">New identities involving Bernoulli and Euler polynomials</a>, arXiv:math/0407363 [math.NT], 2004.
%e B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, 0, -691/2730, ...
%e n*(n+1)*B_n gives the sequence 0, -1, 1, 0, -2/3, 0, 1, 0, -12/5, 0, 25/3, 0, -1382/35, 0, 245, 0, -28936/15, ...
%Y Cf. A002427/A006955.
%K sign,frac
%O 0,3
%A _Seiichi Manyama_, Aug 05 2017
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