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 A182916 #13 Feb 16 2025 08:33:13
%S A182916 1,1,-31,-139,9871,324179,-8225671,-69685339,1674981058019,
%T A182916 24279707153761,-25107254122618741,-1539511255447387949,
%U A182916 181685125700898353671,368622611536873334281,-538867967772767903436298889
%N A182916 Numerators of an asymptotic series for the factorial function (S. Wehmeier).
%C A182916 W_n = A182916(n)/A182917(n). These rational numbers provide the coefficients for an asymptotic expansion of the factorial function. It is a generalization of Gosper's approximation.
%H A182916 Peter Luschny, Approximations to the factorial function, <a href="http://oeis.org/wiki/User:Peter_Luschny/FactorialFunction">Factorial Function</a>.
%H A182916 W. Wang, <a href="http://dx.doi.org/10.1016/j.jnt.2015.12.016">Unified approaches to the approximations of the gamma function</a>, J. Number Theory (2016).
%H A182916 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingsApproximation.html">Stirling's Approximation</a>.
%F A182916 Let A = Sum_{k>=0} W[k]/n^k, then n! ~ sqrt(2Pi*(n+A))*(n/e)^n.
%e A182916 W_0 = 1/6, W_1 = 1/72, W_2 = -31/6480, W_3 = -139/155520, W_4 = 9871/6531840.
%Y A182916 Cf. A182917.
%K A182916 sign,frac
%O A182916 0,3
%A A182916 _Peter Luschny_, Mar 09 2011