A182916 Numerators of an asymptotic series for the factorial function (S. Wehmeier).

1, 1, -31, -139, 9871, 324179, -8225671, -69685339, 1674981058019, 24279707153761, -25107254122618741, -1539511255447387949, 181685125700898353671, 368622611536873334281, -538867967772767903436298889

Offset

0,3

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. A182917.

Sequence in context: A165568 A141950 A201960 * A233303 A185521 A228261

Adjacent sequences: A182913 A182914 A182915 * A182917 A182918 A182919

Keyword

sign,frac

Author

Peter Luschny, Mar 09 2011

Status

approved