A384689 E.g.f. A(x) satisfies A(x) = exp( x*A(x)^2 * A(x*A(x)) ).

1, 1, 7, 106, 2593, 89796, 4085029, 232694806, 16053415249, 1308960150472, 123811136509861, 13387049625793746, 1635128238889494793, 223420020463904387020, 33872693045213102767093, 5658826351169923606739206, 1035543935182601250745181089, 206506472947550295487980305424

Offset: 0

Author

Seiichi Manyama, Jun 07 2025

Keywords

• nonn

Crossrefs

Column k=1 of A384690.

Cf. A140049.

Programs

Mathematica

terms = 18; A[] = 0; Do[A[x] = Exp[x*A[x]^2*A[x*A[x]]] + O[x]^terms // Normal, terms]; Range[0,terms-1]!CoefficientList[A[x], x] (* Stefano Spezia, Jun 07 2025 *)

PARI

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

Formula

See A384690.