login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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.
3

%I #3 Mar 30 2012 18:36:58

%S 1,1,3,12,56,283,1503,8262,46591,267984,1565949,9269559,55465035,

%T 334919996,2038268620,12489068727,76980573203,476994419698,

%U 2969444848029,18563305700106,116485903375761,733457500802353

%N 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.

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

%o (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)}

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 17 2006