|
%I #9 Sep 23 2016 12:39:50
%S 6,72,6480,155520,6531840,1175731200,7054387200,338610585600,
%T 1005673439232000,84476568895488000,6589172373848064000,
%U 2372102054585303040000,14232612327511818240000,170791347930141818880000,9145876681659094401024000000
%N Denominators of an asymptotic series for the factorial function (S. Wehmeier).
%C 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 Peter Luschny, Approximations to the factorial function, <a href="https://oeis.org/wiki/User:Peter_Luschny/FactorialFunction">Factorial Function</a>.
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StirlingsApproximation.html">Stirling's Approximation</a>.
%F Let A = Sum_{k>=0} W[k]/n^k, then n! ~ sqrt(2Pi*(n+A))*(n/e)^n.
%e W_0 = 1/6, W_1 = 1/72, W_2 = -31/6480, W_3 = -139/155520, W_4 = 9871/6531840.
%Y Cf. A182916.
%K nonn,frac
%O 0,1
%A _Peter Luschny_, Mar 09 2011
| 