A120921 G.f. satisfies: A(x) = G(x) * A(x^4*G(x)^9), where G(x) is the g.f. of A001764: G(x) = 1 + x*G(x)^3.

1, 1, 3, 12, 56, 283, 1503, 8262, 46591, 267984, 1565949, 9269559, 55465035, 334919996, 2038268620, 12489068727, 76980573203, 476994419698, 2969444848029, 18563305700106, 116485903375761, 733457500802353

Offset: 0

Author

Paul D. Hanna, Jul 17 2006

Keywords

• nonn

Comments

Self-convolution cube equals A120920, which equals column 0 of triangle A120919 (cascadence of (1+x)^3).

Crossrefs

Cf. A120919, A120920, A001764; A001764 (ternary trees).

Programs

PARI

{a(n)=local(A=1+x,G=(1/x*serreverse(x/(1+x+x*O(x^n))^3))^(1/3)); for(i=0,n,A=G*subst(A,x,x^4*G^9 +x*O(x^n)));polcoeff(A,n,x)}