A120920 G.f. satisfies: A(x) = G(x)^3 * A(x^4*G(x)^9), where G(x) is the g.f. of the number of ternary trees (A001764): G(x) = 1 + x*G(x)^3.

1, 3, 12, 55, 276, 1464, 8058, 45543, 262626, 1538607, 9130446, 54761628, 331403447, 2021021082, 12407102937, 76611488305, 475493441604, 2964664310319, 18560063203353, 116621922800283, 735236268006654

Offset

0,2

Comments

Column 0 of triangle A120919 (cascadence of (1+x)^3).

Links

Table of n, a(n) for n=0..20.

Example

A(x) = 1 + 3*x + 12*x^2 + 55*x^3 + 276*x^4 + 1464*x^5 + 8058*x^6 +...
= G(x)^3 * A(x^4*G(x)^9) where
G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
is g.f. of A001764: G(x) = 1 + x*G(x)^3.

Prog

(PARI) {a(n)=local(A=1+x, G=(1/x*serreverse(x/(1+3*x+3*x^2+x^3+x*O(x^n))))^(1/3)); for(i=0, n, A=G^3*subst(A, x, x^4*G^9 +x*O(x^n))); polcoeff(A, n, x)}

Crossrefs

Cf. A120919, A120921 (cube-root), A120922, A120923; A001764; variants: A092684, A092687, A120895, A120899, A120920.

Sequence in context: A216494 A366100 A342283 * A179487 A350265 A263533

Adjacent sequences: A120917 A120918 A120919 * A120921 A120922 A120923

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2006

Status

approved