A385059 E.g.f. A(x) satisfies A(x) = exp(x*A(x)/A(-x*A(x))^2).

1, 1, 7, 40, 397, 2336, -46601, -2661896, -125428775, -3724273664, -90080842229, 1096530753176, 400257318802213, 36023363702572000, 2951479723885410943, 178834401869241704056, 8444450128124255913649, -59239960097902788177664, -92000068200778017857238125

Offset: 0

Author

Seiichi Manyama, Jun 16 2025

Keywords

• sign

Crossrefs

Column k=1 of A385062.

Cf. A052752, A384983.

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, 2*j)));

Formula

See A385062.