%I #11 Sep 23 2016 12:25:18
%S 1,1,3,18029,6272051,2399400481893,2360892742128702160071689,
%T 1225408074190853330503870473269754327221,
%U 2111833643474196598745616885237164204175699342833563922769,61021653911740304085897627617156000912701780196503645897652921180865489827779803343
%N Numerators of an asymptotic series for the factorial function.
%C C_n = A182914(n)/A182915(n). These rational numbers provide the coefficients for an asymptotic expansion of the factorial function.
%H L. Feng and W. Wang, <a href="http://dx.doi.org/10.1007/s11075-012-9671-x">Two families of approximations for the gamma function</a>, Numerical Algorithms, Springer 2012.
%H Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/FactorialFunction">Approximations to the 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).
%F Let N = n + 1/2 and p = N^2*C_0/(N+C_1/(N+C_2/(N+C_3/(N+C_4/N)...))), then
%F n! ~ sqrt(2Pi) (p/e)^N.
%e C_0 = 1, C_1 = 1/24, C_2 = 3/80, C_3 = 18029/45360, C_4 = 6272051/14869008.
%Y Cf. A182915 (denominators).
%K nonn,frac
%O 0,3
%A _Peter Luschny_, Mar 08 2011