A153292 G.f.: A(x) = F(x*F(x)^2) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764.

1, 1, 5, 31, 211, 1516, 11295, 86423, 675051, 5361323, 43171480, 351709926, 2894115003, 24022408477, 200918146461, 1691749323232, 14329850844625, 122028162988698, 1044131083377287, 8972696721635997, 77408293908402336

Offset: 0

Author

Paul D. Hanna, Jan 14 2009

Keywords

• nonn

Examples

			G.f.: A(x) = F(x*F(x)^2) = 1 + x + 5*x^2 + 31*x^3 + 211*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 +...
		

Crossrefs

Cf. A001764, A000108; A153293.

Programs

PARI

{a(n)=if(n==0,1,sum(k=0,n,binomial(3*k+1,k)/(3*k+1)*binomial(3*(n-k)+2*k,n-k)*2*k/(3*(n-k)+2*k)))}

Formula

a(n) = Sum_{k=0..n} C(3k+1,k)/(3k+1) * C(3n-k,n-k)*2k/(3n-k) for n>0 with a(0)=1.

G.f. satisfies: A(x) = 1 + x*F(x)^2*A(x)^3 where F(x) is the g.f. of A001764.

G.f. satisfies: A(x/G(x)) = F(x*G(x)) where G(x) = F(x/G(x)) is the g.f. of A000108 and F(x) is the g.f. of A001764.