A385058 E.g.f. A(x) satisfies A(x) = exp(x*A(x)/A(-x*A(x))).

1, 1, 5, 31, 333, 3841, 57463, 836109, 11138921, 14908465, -10091931669, -687827361011, -40151825312387, -2071761364164231, -106488772704576961, -5002145237145820979, -203989286928198178863, -4164191357488024315679, 500440079223957671460307, 99906607739361143393212941

Offset: 0

Author

Seiichi Manyama, Jun 16 2025

Keywords

• sign

Crossrefs

Column k=1 of A385061.

Cf. A052750, A384982.

Programs

PARI

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

Formula

See A385061.