cp's OEIS Frontend

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.

A182915 Denominators of an asymptotic series for the factorial function.

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%I A182915 #11 Sep 23 2016 12:25:07
%S A182915 1,24,80,45360,14869008,1809260919664,1893786570223344344811120,
%T A182915 434929389096410771976850108581894819120,
%U A182915 842034816645697476736023674501481289989461304853979754032,12493081332932849693690211275701739272086387015742438665176379932658393033468667344
%N A182915 Denominators of an asymptotic series for the factorial function.
%C A182915 C_n = A182914(n)/A182915(n). These rational numbers provide the coefficients for an asymptotic expansion of the factorial function.
%H A182915 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 A182915 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/FactorialFunction">Approximations to the factorial function</a>.
%H A182915 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 A182915 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 A182915 n! ~ sqrt(2Pi) (p/e)^N.
%e A182915 C_0 = 1, C_1 = 1/24, C_2 = 3/80, C_3 = 18029/45360, C_4 = 6272051/14869008.
%Y A182915 Cf. A182914 (numerators).
%K A182915 nonn,frac
%O A182915 0,2
%A A182915 _Peter Luschny_, Mar 08 2011