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A002427 Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
(Formerly M2510 N0993)
9
1, 1, -1, 1, -3, 5, -691, 35, -3617, 43867, -1222277, 854513, -1181820455, 76977927, -23749461029, 8615841276005, -84802531453387, 90219075042845, -26315271553053477373, 38089920879940267, -261082718496449122051, 1520097643918070802691 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Doubled a(n+2)=-1,1,-3,5,-691,35, "gives" A140351(n+4) secondary Bernoulli twin numbers. Thanks to R. J. Mathar. [Paul Curtz, Nov 28 2009]

REFERENCES

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.

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).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..314 (terms 0..100 from T. D. Noe)

L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93.

M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193.

Index entries for sequences related to Bernoulli numbers.

EXAMPLE

(n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...

MATHEMATICA

Numerator[ Table[2(2n + 1)BernoulliB[2n], {n, 1, 21}]]

PROG

(PARI) a(n) = numerator((2*n+1)*bernfrac(2*n)); \\ Michel Marcus, Aug 06 2017

CROSSREFS

Denominators are in A006955. Cf. A050925/A050932, A000367/A002445.

Sequence in context: A138584 A277995 A247699 * A136134 A119497 A298094

Adjacent sequences:  A002424 A002425 A002426 * A002428 A002429 A002430

KEYWORD

sign,easy,nice,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 23:39 EDT 2018. Contains 316405 sequences. (Running on oeis4.)