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 A182917 Denominators of an asymptotic series for the factorial function (S. Wehmeier). 3
 6, 72, 6480, 155520, 6531840, 1175731200, 7054387200, 338610585600, 1005673439232000, 84476568895488000, 6589172373848064000, 2372102054585303040000, 14232612327511818240000, 170791347930141818880000, 9145876681659094401024000000 (list; graph; refs; listen; history; text; internal format)
 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 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 * A203433 A008562 A041063 Adjacent sequences:  A182914 A182915 A182916 * A182918 A182919 A182920 KEYWORD nonn,frac AUTHOR Peter Luschny, Mar 09 2011 STATUS approved

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Last modified December 18 11:15 EST 2018. Contains 318219 sequences. (Running on oeis4.)