A064633 a(n) = 3^n*n!*(n+2)!/2!.

1, 9, 216, 9720, 699840, 73483200, 10581580800, 1999918771200, 479980505088000, 142554210011136000, 51319515604008960000, 22016072194119843840000, 11096100385836401295360000, 6491218725714294757785600000, 4362098983680006077231923200000

Offset: 0

Author

Karol A. Penson, Oct 01 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..75

Crossrefs

Cf. A000244, A010791.

Programs

Mathematica

Table[3^n n! (n+2)!/2,{n,0,20}] (* Harvey P. Dale, Feb 25 2015 *)

PARI

{ for (n=0, 75, write("b064633.txt", n, " ", 3^n*n!*(n + 2)!/2) ) } \\ Harry J. Smith, Sep 20 2009

Formula

Hypergeometric g.f.: (1-3*x)^(-3).

a(0)=1, a(n) = n!*subs(x=0, (d^n/dx^n)(-1/((3*x-1)^3))), n = 1, 2, ...

From Amiram Eldar, Sep 27 2022: (Start)

Sum_{n>=0} 1/a(n) = 6*BesselI(2,2/sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 6*BesselJ(2,2/sqrt(3)). (End)