A065961 a(n) = (3*n - 1)!*n/2.

1, 120, 60480, 79833600, 217945728000, 1067062284288000, 8515157028618240000, 103408066955539906560000, 1814811575069725360128000000, 44208809968698509772718080000000, 1447219603135314415919699066880000000, 61998887798316869577999908025139200000000

Offset: 1

Author

Len Smiley and George E. Antoniou, Dec 08 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A100732.

Programs

Magma

[ Factorial(3*n)/6: n in [1..62] ]; // Vincenzo Librandi, Apr 24 2011

Mathematica

(3*Range[15])!/6 (* Paolo Xausa, Feb 16 2024 *)

PARI

{ for (n=1, 60, a=(3*n - 1)!*n/2; write("b065961.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 04 2009

Formula

a(n) = (3*n)! / 6.

a(n) - 3*n*(3*n-1)*(3*n-2)*a(n-1) = 0. - R. J. Mathar, Oct 31 2015

From Amiram Eldar, Feb 17 2024: (Start)

Sum_{n>=1} 1/a(n) = 2*e - 6 + 4*cos(sqrt(3)/2)/sqrt(e).

Sum_{n>=1} (-1)^(n+1)/a(n) = 6 - 2/e - 4*sqrt(e)*cos(sqrt(3)/2). (End)