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 A290533 Numerator of 2*n*(2*n+1) B_{2*n}, where B_n are the Bernoulli numbers. 1
 0, 1, -2, 1, -12, 25, -1382, 245, -28936, 131601, -2444554, 9399643, -4727281820, 1000713051, -332492454406, 43079206380025, -1356840503254192, 1533724275728365, -157891629318320864238, 723708496718865073, -1044330873985796488204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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..314 Y. Matiyasevich, Identities with Bernoulli numbers, 1997. H. Pan and Z. W. Sun, New identities involving Bernoulli and Euler polynomials, arXiv:math/0407363 [math.NT], 2004. EXAMPLE 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, ... 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, ... CROSSREFS Cf. A002427/A006955. Sequence in context: A061081 A007368 A054677 * A012929 A013161 A012926 Adjacent sequences: A290530 A290531 A290532 * A290534 A290535 A290536 KEYWORD sign,frac AUTHOR Seiichi Manyama, Aug 05 2017 STATUS approved

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Last modified June 2 07:25 EDT 2023. Contains 363081 sequences. (Running on oeis4.)