A290534 Denominator of 2*n*(2*n+1) B_{2*n}, where B_n are the Bernoulli numbers.

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, 15, 133, 145, 3, 31031, 1, 51, 161, 5, 33, 319865, 1, 15, 7, 7667, 3, 16211, 1, 345, 6479, 235, 3, 7735, 1, 33, 7, 53, 3, 319865, 23, 7395, 7, 295, 3, 7055321, 1, 3, 817

Offset: 0

Author

Seiichi Manyama, Aug 05 2017

Keywords

• nonn
• frac

Comments

In 1997, Matiyasevich found the following identity;

(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.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500
• Y. Matiyasevich, Identities with Bernoulli numbers, 1997.
• Hao Pan and Zhi-Wei Sun, New identities involving Bernoulli and Euler polynomials, Journal of Combinatorial Theory, Series A Volume 113, Issue 1, January 2006, Pages 156-175.

Crossrefs

Cf. A002427/A006955.