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A114721 Denominator of expansion of RiemannSiegelTheta(t) about infinity. 3
48, 5760, 80640, 430080, 1216512, 1476034560, 2555904, 8021606400, 64012419072, 131491430400, 3472883712, 25282593423360, 20132659200, 25222195445760, 2675794690179072, 2172909854392320, 6803228196864 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

H. M. Edwards, Riemann's Zeta Function, Dover Publications, New York, 1974 (ISBN 978-0-486-41740-0), p. 120.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, arXiv:1608.04834 [math.NA], 2016.

Simon Plouffe, On the values of the functions zeta and gamma, arXiv preprint arXiv:1310.7195, 2013.

Eric Weisstein's World of Mathematics, Riemann-Siegel Function

FORMULA

a(n) is the denominator of (-1)^n*BernoulliB(2*n, 1/2)/(4*n*(2*n-1)).

EXAMPLE

RiemannSiegelTheta(t) = -Pi/8 + t*(-1/2 - log(2)/2 - log(Pi)/2 - log(t^(-1))/2) + 1/(48*t) + 7/(5760*t^3) + 31/(80640*t^5) + ...

MATHEMATICA

a[n_] := (-1)^n*BernoulliB[2*n, 1/2]/(4*n*(2*n-1)) // Denominator; Table[a[n], {n, 1, 16}] (* Jean-Fran├žois Alcover, Aug 04 2014 *)

PROG

(PARI) a(n) = denominator(subst(bernpol(2*n), x, 1/2)/(4*n*(2*n-1))); \\ Michel Marcus, Jun 20 2018

CROSSREFS

Cf. A036282, A282898 (numerators), A282899.

Sequence in context: A321940 A222846 A265666 * A057868 A269179 A276098

Adjacent sequences:  A114718 A114719 A114720 * A114722 A114723 A114724

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Dec 27 2005

STATUS

approved

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Last modified December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)