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 A182915 Denominators of an asymptotic series for the factorial function. 3
 1, 24, 80, 45360, 14869008, 1809260919664, 1893786570223344344811120, 434929389096410771976850108581894819120, 842034816645697476736023674501481289989461304853979754032, 12493081332932849693690211275701739272086387015742438665176379932658393033468667344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS C_n = A182914(n)/A182915(n). These rational numbers provide the coefficients for an asymptotic expansion of the factorial function. LINKS L. Feng and W. Wang, Two families of approximations for the gamma function, Numerical Algorithms, Springer 2012. Peter Luschny, Approximations to the factorial function. W. Wang, Unified approaches to the approximations of the gamma function, J. Number Theory (2016). FORMULA Let N = n + 1/2 and p = N^2*C_0/(N+C_1/(N+C_2/(N+C_3/(N+C_4/N)...))), then n! ~ sqrt(2Pi) (p/e)^N. EXAMPLE C_0 = 1, C_1 = 1/24, C_2 = 3/80, C_3 = 18029/45360, C_4 = 6272051/14869008. CROSSREFS Cf. A182914 (numerators). Sequence in context: A211589 A211597 A318988 * A030622 A063456 A265646 Adjacent sequences: A182912 A182913 A182914 * A182916 A182917 A182918 KEYWORD nonn,frac AUTHOR Peter Luschny, Mar 08 2011 STATUS approved

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Last modified December 8 03:48 EST 2022. Contains 358672 sequences. (Running on oeis4.)