OFFSET
0,3
FORMULA
EXAMPLE
G.f.: A(x) = F(x*G(x)^3) = 1 + x + 6*x^2 + 39*x^3 + 272*x^4+... where
F(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*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 +...
G(x)^3 = 1 + 3*x + 9*x^2 + 28*x^3 + 90*x^4 + 297*x^5 + 1001*x^6 +...
A(x)^2 = 1 + 2*x + 13*x^2 + 90*x^3 + 658*x^4 + 5014*x^5 +...
A(x)^3 = 1 + 3*x + 21*x^2 + 154*x^3 + 1176*x^4 + 9264*x^5 +...
G(x)^3*A(x)^3 = 1 + 6*x + 39*x^2 + 272*x^3 + 2001*x^4 + 15333*x^5 +...
PROG
(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*binomial(2*(n-k)+3*k, n-k)*3*k/(2*(n-k)+3*k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 15 2009
STATUS
approved