A384894 G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^2.

1, 1, 2, 1, -4, -14, -30, 12, 330, 1139, 2226, -2288, -39646, -163742, -410900, -89273, 5352720, 31177720, 114624554, 234094417, -312845870, -5584935715, -32878240028, -127407695297, -315375599410, 24759230680, 6177102106748, 44838273448641, 220383314338200

Offset: 0

Author

Seiichi Manyama, Jun 12 2025

Keywords

• sign

Crossrefs

Column k=1 of A384899.

Cf. A000108, A213094, A213095, A384895.

Cf. A213091.

Programs

PARI

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

Formula

See A384899.