OFFSET
0,1
COMMENTS
A binomial sequence that produces Pi: 1/Pi= Binomial[2*n+1,n+1/2]/(2*n+1)!!
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..100
FORMULA
a(n) = 4 * A051189(n).
From Ilya Gutkovskiy, Aug 22 2016: (Start)
E.g.f.: 4/(1 - 8*x).
a(n) ~ sqrt(Pi)*2^(3*n+5/2)*n^(n+1/2)/exp(n). (End)
MATHEMATICA
Table[(2*n + 1)!!*Pi*Gamma[2*n + 2]/(Gamma[n + 3/2]^2), {n, 0, 20}]
PROG
(PARI) a(n) = 4*n!*8^n; \\ Michel Marcus, Aug 22 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Dec 28 2008
STATUS
approved