%I #19 Dec 15 2015 07:25:34

%S 1,-1,-1,157,65911,-918227,-234932171,592642957,149463069056137,

%T -16648792617135289,-286497627060094895989,3538603031642540133299,

%U 57674522110226646157873673,-713986824035720029666660757,-6478234620955890989297122598683

%N Numerators in the asymptotic expansion of the Barnes G-function.

%H G. C. Greubel and D. Turner, <a href="/A260447/b260447.txt">Table of n, a(n) for n = 0..175</a>

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.

%F G(x) ~ exp^(-3*x^2/4 + x + zeta'(-1)) * x^(x^2/2 - x + 5/12) * (2*Pi)^((x-1)/2) * (1 + (-1/12)/x + (-1/1440)/x^2 + (157/51840)/x^3 + (65911/87091200)/x^4 + ...).

%t Numerator[Exp[Series[LogBarnesG[x] - 1/12 - x + 3 x^2/4 + Log[Glaisher] + Log[2 Pi]/2 - x Log[2 Pi]/2 - 5 Log[x]/12 + x Log[x] - x^2 Log[x]/2, {x, Infinity, 20}]][[3]]]

%Y Cf. A260448 (denominators), A000178, A001163, A001164.

%K sign,frac

%O 0,4

%A _Vladimir Reshetnikov_, Nov 10 2015