A384740 E.g.f. A(x) satisfies A(x) = exp( x * A(x*A(x)^3) ).

1, 1, 3, 34, 665, 20556, 901417, 52455250, 3885229665, 355223077336, 39166024398641, 5113078496932374, 778733373110049601, 136679150176555902436, 27360426865918664532393, 6191378995818235673842546, 1571577905668087973855557313, 444441393534829346316950781744

Offset: 0

Author

Seiichi Manyama, Jun 08 2025

Keywords

• nonn

Crossrefs

Column k=1 of A384742.

Cf. A000272, A162659, A384739.

Cf. A384720.

Programs

PARI

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

Formula

See A384742.