A384577 G.f. A(x) satisfies A(x) = ( 1 + x * A(x*A(x))^(1/3) )^3.

1, 3, 6, 19, 78, 411, 2617, 19251, 160254, 1482400, 15035622, 165545253, 1963006576, 24908182305, 336397711074, 4813816122917, 72704962269990, 1155070280657286, 19245587072017468, 335418172582313610, 6100293082529588802, 115532044092709366555, 2274095852526512246841

Offset: 0

Author

Seiichi Manyama, Jun 04 2025

Keywords

• nonn

Crossrefs

Column k=3 of A384581.

Programs

PARI

a(n, k=3) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-3*j+k, j)/(3*n-3*j+k)*a(n-j, j)));

Formula

See A384581.

G.f.: B(x)^3, where B(x) is the g.f. of A143501.