login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046988 Numerators of Taylor series expansion of log(x/sin(x)). For n>0, numerators of zeta(2*n)/Pi^(2*n). 13
0, 1, 1, 1, 1, 1, 691, 2, 3617, 43867, 174611, 155366, 236364091, 1315862, 6785560294, 6892673020804, 7709321041217, 151628697551, 26315271553053477373, 308420411983322, 261082718496449122051, 3040195287836141605382, 5060594468963822588186 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Equivalently, numerator of (-1)^n*2^(2*n-1)*Bernoulli(2*n)/(2*n)!. - Lekraj Beedassy, Jun 26 2003

Numerator(Zeta(0)/Pi^0) = -1. [Artur Jasinski, Mar 11 2010]

REFERENCES

L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205

T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 222, series for log(H(x)/x).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.

CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.

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. 84.

LINKS

J.P. Martin-Flatin, Table of n, a(n) for n = 0..250

I. Song, A recursive formula for even order harmonic series, J. Computational and Appl. Math., 21 (1988), 251-256.

Wolfram Research, Some values of zeta(n)

Wolfram Research, A Formula for Zeta(2n)

EXAMPLE

log(x/sin(x)) = 1/6*x^2+1/180*x^4+1/2835*x^6+1/37800*x^8+1/467775*x^10+...

MAPLE

seq(numer(Zeta(2*n)/Pi^(2*n)), n=1..24); # Martin Renner, Sep 07 2016

MATHEMATICA

Table[Numerator[Zeta[2 n]/Pi^(2 n)], {n, 1, 30}] (* Artur Jasinski, Mar 11 2010 *)

CROSSREFS

Cf. A046989, A002432.

Sequence in context: A001067 A141590 A276594 * A189683 A029825 A180320

Adjacent sequences:  A046985 A046986 A046987 * A046989 A046990 A046991

KEYWORD

nonn,easy,frac,nice

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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 19:20 EST 2016. Contains 278755 sequences.