A384617 E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x))^2 ).

1, 1, 5, 13, -63, -2279, -51167, -423387, 13717889, 885044593, 37051519041, 779965433149, -14179999608959, -2798466635425239, -224720509492366495, -11148988922254048619, -300176114650473574143, 18804123010954180467937, 4351564646569010083711105

Offset: 0

Author

Seiichi Manyama, Jun 10 2025

Keywords

• sign

Crossrefs

Column k=1 of A384808.

Cf. A052750, A213110, A213111, A384809, A384810.

Cf. A213108.

Programs

PARI

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

Formula

See A384808.