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

Author

Peter Luschny, Mar 09 2011

Keywords

• nonn
• frac

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.

Examples

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

Links

• 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.

Crossrefs

Cf. A182916.

Formula

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