A290534 - OEIS

%I #16 Aug 07 2017 10:02:40

%S 1,1,3,1,5,3,35,1,15,7,11,3,91,1,15,77,85,3,8645,1,33,1,23,3,1105,11,

%T 15,133,145,3,31031,1,51,161,5,33,319865,1,15,7,7667,3,16211,1,345,

%U 6479,235,3,7735,1,33,7,53,3,319865,23,7395,7,295,3,7055321,1,3,817

%N Denominator 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="/A290534/b290534.txt">Table of n, a(n) for n = 0..500</a>

%H Y. Matiyasevich, <a href="http://logic.pdmi.ras.ru/~yumat/personaljournal/identitybernoulli/bernulli.htm">Identities with Bernoulli numbers</a>, 1997.

%H Hao Pan and Zhi-Wei Sun, <a href="https://doi.org/10.1016/j.jcta.2005.07.008">New identities involving Bernoulli and Euler polynomials</a>, Journal of Combinatorial Theory, Series A Volume 113, Issue 1, January 2006, Pages 156-175.

%Y Cf. A002427/A006955.

%K nonn,frac

%O 0,3

%A _Seiichi Manyama_, Aug 05 2017