A385013 G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x)^2).

1, 1, 2, 4, 9, 19, 37, 52, -25, -630, -3616, -15897, -61476, -215135, -677464, -1823081, -3389900, 2523349, 73121734, 526205851, 2914005085, 14163375846, 62788424920, 255900158756, 945473736954, 3008738746058, 6827204137454, -2853842162077, -171206510083289

Offset: 0

Author

Seiichi Manyama, Jun 15 2025

Keywords

• sign

Crossrefs

Column k=1 of A385017.

Cf. A000108, A213225, A213226, A384951.

Cf. A213091.

Programs

PARI

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

Formula

See A385017.