OFFSET
0,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..75
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)
MATHEMATICA
Table[3^n n! (n+2)!/2, {n, 0, 20}] (* Harvey P. Dale, Feb 25 2015 *)
PROG
(PARI) { for (n=0, 75, write("b064633.txt", n, " ", 3^n*n!*(n + 2)!/2) ) } \\ Harry J. Smith, Sep 20 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Oct 01 2001
STATUS
approved