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 A182914 Numerators of an asymptotic series for the factorial function. 3
 1, 1, 3, 18029, 6272051, 2399400481893, 2360892742128702160071689, 1225408074190853330503870473269754327221, 2111833643474196598745616885237164204175699342833563922769, 61021653911740304085897627617156000912701780196503645897652921180865489827779803343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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. A182915 (denominators). Sequence in context: A124393 A116182 A155180 * A203182 A128121 A112406 Adjacent sequences:  A182911 A182912 A182913 * A182915 A182916 A182917 KEYWORD nonn,frac AUTHOR Peter Luschny, Mar 08 2011 STATUS approved

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Last modified September 21 21:21 EDT 2018. Contains 315262 sequences. (Running on oeis4.)