A384145 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x*A(x)^3) ).

1, 1, 2, 8, 44, 298, 2359, 21112, 209175, 2262121, 26431042, 331096188, 4419824468, 62565545535, 935341395343, 14716294925179, 242945752432294, 4197094127399756, 75698807290515322, 1422350601250404765, 27788515730656558613, 563512508612712699574, 11841983002490204813514

Offset: 0

Author

Seiichi Manyama, Jun 06 2025

Keywords

• nonn

Crossrefs

Column k=1 of A384652.

Cf. A110447, A162661, A384649, A384650.

Programs

PARI

a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-2*j+k, j)/(3*n-2*j+k)*a(n-j, j)));

Formula

See A384652.