A182915 Denominators of an asymptotic series for the factorial function.

1, 24, 80, 45360, 14869008, 1809260919664, 1893786570223344344811120, 434929389096410771976850108581894819120, 842034816645697476736023674501481289989461304853979754032, 12493081332932849693690211275701739272086387015742438665176379932658393033468667344

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

Table of n, a(n) for n=0..9.

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