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A114721 Denominator of expansion of RiemannSiegelTheta(t) about infinity. 3

%I

%S 48,5760,80640,430080,1216512,1476034560,2555904,8021606400,

%T 64012419072,131491430400,3472883712,25282593423360,20132659200,

%U 25222195445760,2675794690179072,2172909854392320,6803228196864

%N Denominator of expansion of RiemannSiegelTheta(t) about infinity.

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

%H Seiichi Manyama, <a href="/A114721/b114721.txt">Table of n, a(n) for n = 1..1000</a>

%H R. P. Brent, <a href="http://arxiv.org/abs/1608.04834"> Asymptotic approximation of central binomial coefficients with rigorous error bounds</a>, arXiv:1608.04834 [math.NA], 2016.

%H Simon Plouffe, <a href="http://arxiv.org/abs/1310.7195">On the values of the functions zeta and gamma</a>, arXiv preprint arXiv:1310.7195, 2013.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Riemann-SiegelFunctions.html">Riemann-Siegel Function</a>

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

%e 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) + ...

%t 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 *)

%o (PARI) a(n) = denominator(subst(bernpol(2*n), x, 1/2)/(4*n*(2*n-1))); \\ _Michel Marcus_, Jun 20 2018

%Y Cf. A036282, A282898 (numerators), A282899.

%K nonn,frac

%O 1,1

%A _Eric W. Weisstein_, Dec 27 2005

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