A182917 Denominators of an asymptotic series for the factorial function (S. Wehmeier).

6, 72, 6480, 155520, 6531840, 1175731200, 7054387200, 338610585600, 1005673439232000, 84476568895488000, 6589172373848064000, 2372102054585303040000, 14232612327511818240000, 170791347930141818880000, 9145876681659094401024000000

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..14.

Peter Luschny, Approximations to the factorial function, Factorial Function.

W. Wang, Unified approaches to the approximations of the gamma function, J. Number Theory (2016).

Eric Weisstein's World of Mathematics, Stirling's Approximation.

Formula

Let A = Sum_{k>=0} W[k]/n^k, then n! ~ sqrt(2Pi*(n+A))*(n/e)^n.

Example

W_0 = 1/6, W_1 = 1/72, W_2 = -31/6480, W_3 = -139/155520, W_4 = 9871/6531840.

Crossrefs

Cf. A182916.

Sequence in context: A132878 A006585 A166472 * A328814 A203433 A008562

Adjacent sequences: A182914 A182915 A182916 * A182918 A182919 A182920

Keyword

nonn,frac

Author

Peter Luschny, Mar 09 2011

Status

approved