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 A182916 Numerators of an asymptotic series for the factorial function (S. Wehmeier). 3
 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 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

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Last modified September 22 09:45 EDT 2017. Contains 292337 sequences.