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A046988 Numerators of zeta(2*n)/Pi^(2*n). 21
-1, 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+1)*2^(2*n-1)*Bernoulli(2*n)/(2*n)!. - Lekraj Beedassy, Jun 26 2003
An old name erroneously included "Numerators of Taylor series expansion of log(x/sin(x))"; that is now submitted as a distinct sequence A283301. - Vladimir Reshetnikov, Mar 04 2017
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
Masato Kobayashi and Shunji Sasaki, Values of zeta-one functions at positive even integers, arXiv:2202.11835 [math.NT], 2022. See p. 4.
Ellise Parnoff and A. Raghuram, Ramanujan's congruence primes, arXiv:2403.03345 [math.NT], 2024.
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
Numerator(zeta(0)/Pi^0) = -1. - Artur Jasinski, Mar 11 2010
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, 0, 30}] (* Artur Jasinski, Mar 11 2010 *)
CROSSREFS
Cf. A002432 (denominators), A283301, A266214.
Sequence in context: A141590 A276594 A283301 * A189683 A029825 A180320
KEYWORD
sign,easy,frac,nice,changed
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)