A002427 Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers. (Formerly M2510 N0993)

1, 1, -1, 1, -3, 5, -691, 35, -3617, 43867, -1222277, 854513, -1181820455, 76977927, -23749461029, 8615841276005, -84802531453387, 90219075042845, -26315271553053477373, 38089920879940267, -261082718496449122051, 1520097643918070802691

Offset

0,5

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: 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...

Maple

gf := z / (1 - exp(-z)): ser := series(gf, z, 84):
seq(numer((n+1)!*coeff(ser, z, n)), n=0..42, 2); # Peter Luschny, Aug 29 2020

Mathematica

Table[Numerator[2(2n+1)BernoulliB[2n]], {n, 1, 30}]

Prog

(PARI) a(n) = numerator((2*n+1)*bernfrac(2*n)); \\ Michel Marcus, Aug 06 2017
(Magma) [Numerator((2*n+1)*Bernoulli(2*n)): n in [1..30]]; // G. C. Greubel, Jul 03 2019
(Sage) [numerator((2*n+1)*bernoulli(2*n)) for n in (1..30)] # G. C. Greubel, Jul 03 2019

Crossrefs

Denominators are in A006955.

Cf. A050925/A050932, A000367/A002445.

Sequence in context: A354245 A247699 A320939 * A350036 A136134 A119497

Adjacent sequences: A002424 A002425 A002426 * A002428 A002429 A002430

Keyword

sign,easy,nice,frac

Author

N. J. A. Sloane

Status

approved