A260447 Numerators in the asymptotic expansion of the Barnes G-function.

1, -1, -1, 157, 65911, -918227, -234932171, 592642957, 149463069056137, -16648792617135289, -286497627060094895989, 3538603031642540133299, 57674522110226646157873673, -713986824035720029666660757, -6478234620955890989297122598683

Offset

0,4

Links

G. C. Greubel and D. Turner, Table of n, a(n) for n = 0..175

Eric Weisstein's World of Mathematics, Barnes G-Function.

Wikipedia, Barnes G-function.

Formula

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 + ...).

Mathematica

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]]]

Crossrefs

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

Sequence in context: A213469 A074220 A015265 * A369007 A345511 A048930

Adjacent sequences: A260444 A260445 A260446 * A260448 A260449 A260450

Keyword

sign,frac

Author

Vladimir Reshetnikov, Nov 10 2015

Status

approved