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A182916
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Numerators of an asymptotic series for the factorial function (S. Wehmeier).
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3
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1, 1, -31, -139, 9871, 324179, -8225671, -69685339, 1674981058019, 24279707153761, -25107254122618741, -1539511255447387949, 181685125700898353671, 368622611536873334281, -538867967772767903436298889
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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FORMULA
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Let A = Sum_{k>=0} W[k]/n^k, then n! ~ sqrt(2Pi*(n+A))*(n/e)^n.
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EXAMPLE
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W_0 = 1/6, W_1 = 1/72, W_2 = -31/6480, W_3 = -139/155520, W_4 = 9871/6531840.
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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