A165457 a(n) = (2*n+1)!*(2*n+3)/3.

1, 10, 280, 15120, 1330560, 172972800, 31135104000, 7410154752000, 2252687044608000, 851515702861824000, 391697223316439040000, 215433472824041472000000, 139600890389978873856000000

Offset: 0

Author

Jaume Oliver Lafont, Sep 20 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..223

Crossrefs

Cf. A133942, A143624.

Cf. A135003. [Jaume Oliver Lafont, Oct 03 2009]

Programs

GAP

List([0..12],n->Factorial(2*n+1)*(2*n+3)/3); # Muniru A Asiru, Oct 21 2018

Magma

[Factorial(2*n+1)*(2*n+3)/3: n in [0..30]]; // G. C. Greubel, Oct 20 2018

Maple

seq(factorial(2*n+1)*(2*n+3)/3,n=0..12); # Muniru A Asiru, Oct 21 2018

Mathematica

Table[(2*n + 1)!*(2*n + 3)/3, {n, 0, 30}] (* G. C. Greubel, Oct 20 2018 *)

PARI

a(n)=(2*n+1)!*(2*n+3)/3

Python

import math
for n in range(0, 12): print(int(math.factorial(2*n+1)*(2*n+3)/3), end=', ') # Stefano Spezia, Oct 21 2018

Formula

a(n) = 2*n*(2*n+3)*a(n-1).

Sum_{k>=0} 1/a(k) = 3/e = A135003.

G.f.: 3F0(1,1,5/2;;4x). - R. J. Mathar, Oct 15 2009

Sum_{k>=0} (-1)^k/a(k) = 3*(sin(1)-cos(1)) = (-3)*A143624. - Amiram Eldar, Apr 12 2021

Extensions

frac keyword removed by Jaume Oliver Lafont, Nov 02 2009