A121399 G.f. satisfies: A(x) = G(x)*A(x^2*G(x)) where G(x) is the g.f. of the Motzkin numbers (A001006): G = (1 + x*G + x^2*G^2).

1, 1, 3, 6, 17, 42, 114, 302, 827, 2263, 6275, 17468, 48967, 137834, 389738, 1105861, 3148240, 8987989, 25726635, 73808069, 212196040, 611219900, 1763659860, 5097131364, 14752847173, 42757853357, 124080269331, 360493591232

Offset: 0

Author

Paul D. Hanna, Jul 27 2006

Keywords

• nonn

Comments

Equals column 0 of triangle A121400.

Examples

			A(x) = 1 + x + 3*x^2 + 6*x^3 + 17*x^4 + 42*x^5 + 114*x^6 +...
The g.f. of the Motzkin numbers begins:
G(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 21*x^5 + 51*x^6 + 127*x^7 +...
		

Crossrefs

Cf. A121400 (triangle), A121398 (main diagonal), A001006 (Motzkin).

Programs

PARI

{a(n)=local(F=1+x+x^2,G=serreverse(x/(F+x^2*O(x^n)))/x,H=1+x,A); for(i=0,n,H=G*subst(H,x,x^2*G)+x^2*O(x^n)); A=(x*H-y*subst(H,x,x*y))/(x*subst(F,x,y)-y); polcoeff(polcoeff(A,n,x),0,y)}