A120900 G.f. satisfies: A(x) = C(x)*A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).

1, 1, 2, 6, 19, 62, 209, 722, 2539, 9054, 32654, 118876, 436171, 1611067, 5984943, 22344455, 83786875, 315397144, 1191324649, 4513742858, 17149228138, 65318912291, 249356597492, 953902701488, 3656057618727, 14037222220896

Offset: 0

Author

Paul D. Hanna, Jul 14 2006

Keywords

• nonn

Comments

Self-convolution equals A120899, which equals column 0 of triangle A120898 (cascadence of 1+2x+x^2).

Examples

			A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 62*x^5 + 209*x^6 + 722*x^7 +...
= C(x) * A(x^3*C(x)^4) where
C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.
		

Crossrefs

Cf. A120898, A120899, A000108.

Programs

PARI

{a(n)=local(A=1+x,C=(1/x*serreverse(x/(1+2*x+x^2+x*O(x^n))))^(1/2)); for(i=0,n,A=C*subst(A,x,x^3*C^4 +x*O(x^n)));polcoeff(A,n,x)}