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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
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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 May 25 07:15 EDT 2024. Contains 372782 sequences. (Running on oeis4.)