login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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, ...

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 03:08 EST 2022. Contains 358353 sequences. (Running on oeis4.)