This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A260447 #20 Feb 16 2025 08:33:26
%S A260447 1,-1,-1,157,65911,-918227,-234932171,592642957,149463069056137,
%T A260447 -16648792617135289,-286497627060094895989,3538603031642540133299,
%U A260447 57674522110226646157873673,-713986824035720029666660757,-6478234620955890989297122598683
%N A260447 Numerators in the asymptotic expansion of the Barnes G-function.
%H A260447 G. C. Greubel and D. Turner, <a href="/A260447/b260447.txt">Table of n, a(n) for n = 0..175</a>
%H A260447 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>.
%H A260447 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>.
%F A260447 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 A260447 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 A260447 Cf. A260448 (denominators), A000178, A001163, A001164.
%K A260447 sign,frac
%O A260447 0,4
%A A260447 _Vladimir Reshetnikov_, Nov 10 2015