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A002427
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Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
(Formerly M2510 N0993)
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4
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1, 1, -1, 1, -3, 5, -691, 35, -3617, 43867, -1222277, 854513, -1181820455, 76977927, -23749461029, 8615841276005, -84802531453387, 90219075042845, -26315271553053477373, 38089920879940267, -261082718496449122051, 1520097643918070802691
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OFFSET
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0,5
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COMMENTS
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Doubled a(n+2)=-1,1,-3,5,-691,35, "gives" A140351(n+4) secondary Bernoulli twin numbers.Thanks to R. J. Mathar. [From Paul Curtz, Nov 28 2009]
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REFERENCES
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L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93.
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
M. Kaneko, "A recurrence formula for the Bernoulli numbers", Proc. Japan Acad., 71 A (1995), 192-193.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
Index entries for sequences related to Bernoulli numbers.
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EXAMPLE
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(n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...
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MATHEMATICA
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Numerator[ Table[2(2n + 1)BernoulliB[2n], {n, 1, 21}]]
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CROSSREFS
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Denominators are in A006955. Cf. A050925/A050932, A000367/A002445.
Sequence in context: A087368 A087670 A138584 * A136134 A119497 A012783
Adjacent sequences: A002424 A002425 A002426 * A002428 A002429 A002430
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KEYWORD
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sign,easy,nice,frac
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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