OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} C(3k+3,k)/(k+1) * C(2n,n-k)*k/n for n>0 with a(0)=1.
G.f. satisfies: A(x*F(x)) = F(x*F(x)^3)^3 = F(F(x)-1)^3 where F(x) is the g.f. of A001764.
EXAMPLE
G.f.: A(x) = F(x*G(x)^2)^3 = 1 + 3*x + 18*x^2 + 118*x^3 + 813*x^4 +... where
F(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
F(x)^2 = 1 + 2*x + 7*x^2 + 30*x^3 + 143*x^4 + 728*x^5 + 3876*x^6 +...
F(x)^3 = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1428*x^5 +...
G(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
G(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...
PROG
(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+3, k)/(k+1)*binomial(2*n, n-k)*k/n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 15 2009
STATUS
approved