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%I #26 Sep 01 2018 21:38:49
%S 1,720,7257600,15676416000,3476402012160000,3320318656512000000,
%T 4919915372473221120000000,4632289550697863577600000000,
%U 507464726196802564122476544000000000,173072180302909506079665684480000000000,49554442037561776763544469977956352000000000000
%N Denominator of the coefficient of z^(-2*n) in the Stirling-like asymptotic expansion of G(z+1), where G(z) is Barnes G-function.
%C G(z+1) ~ A^(-1)*z^(-z^2/2-z/2-1/12)*exp(z^2/4)*(Gamma(z+1))^z*(Sum_{n>=0} b(n)/z^(2*n)), where A is the Glaisher-Kinkelin constant and Gamma is the gamma function.
%C a(n) is the denominator of b(n).
%H Seiichi Manyama, <a href="/A318711/b318711.txt">Table of n, a(n) for n = 0..149</a>
%H Chao-Ping Chen, <a href="https://doi.org/10.1016/j.jnt.2013.08.007">Asymptotic expansions for Barnes G-function</a>, Journal of Number Theory 135 (2014) 36-42.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%F Let B_n be the Bernoulli number, and define the sequence {c_n} by the recurrence
%F c_0 = 1, c_n = (1/(2*n)) * Sum_{k=0..n-1} B_{2*n-2*k+2}*c_k/((2*n-2*k+1)*(2*n-2*k+2)) for n > 0.
%F a(n) is the denominator of c_n.
%e G(z+1) ~ A^(-1)*z^(-z^2/2-z/2-1/12)*exp(z^2/4)*(Gamma(z+1))^z*(1 - 1/(720*z^2) + 1447/(7257600*z^4) - 1559527/(15676416000*z^6) + 366331136219/(3476402012160000*z^8) - 637231027521743/(3320318656512000000*z^10) + ... ).
%Y Cf. A143476, A318710.
%K nonn,frac
%O 0,2
%A _Seiichi Manyama_, Sep 01 2018
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