A182916 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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