OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} C(3k+2,k)*2/(3k+2) * C(2n-k,n-k)*k/(2n-k) for n>0 with a(0)=1.
G.f. satisfies: A(x*F(x)) = F(x*F(x)^2)^2 where F(x) is the g.f. of A001764.
EXAMPLE
G.f.: A(x) = F(x*G(x))^2 = 1 + 2*x + 9*x^2 + 48*x^3 + 278*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 + 7752*x^6 +...
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+2, k)*2/(3*k+2)*binomial(2*(n-k)+k, n-k)*k/(2*(n-k)+k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 15 2009
STATUS
approved