A153511 a(n) = 4 * A051189(n).

4, 32, 512, 12288, 393216, 15728640, 754974720, 42278584320, 2705829396480, 194819716546560, 15585577323724800, 1371530804487782400, 131666957230827110400, 13693363552006019481600

Offset: 0

Author

Roger L. Bagula, Dec 28 2008

Keywords

• nonn

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

Crossrefs

Cf. A051189.

Programs

Mathematica

Table[(2*n + 1)!!*Pi*Gamma[2*n + 2]/(Gamma[n + 3/2]^2), {n, 0, 20}]

PARI

a(n) = 4*n!*8^n; \\ Michel Marcus, Aug 22 2016

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)