OFFSET
0,1
COMMENTS
Coefficients in Stirling's asymptotic expansion of the Gamma function, normalized to integers using factor 3*(2*n)!^2/n!!.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..30
Eric Weisstein's World of Mathematics, Stirling's Series.
FORMULA
MAPLE
h := proc(k) option remember; local j; `if`(k=0, 1,
(h(k-1)/k-add((h(k-j)*h(j))/(j+1), j=1..k-1))/(1+1/(k+1))) end:
g := n -> doublefactorial(2*n-1)*(2*n)!^2/doublefactorial(n):
seq(3*h(2*n)*g(n), n=0..12); # Peter Luschny, Nov 05 2015
MATHEMATICA
Table[3 (2n)!^2/n!! (6n+1)!!/4^n Sum[(-1)^m 2^k StirlingS2[2n+k+m, m]/((2n+2k+1) (2n+k+m)! (2n-k)! (k-m)!), {k, 0, 2n}, {m, 0, k}], {n, 0, 12}]
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Reshetnikov, Nov 04 2015
STATUS
approved