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-François 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
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Dec 27 2005
STATUS
approved