A385014 G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^2.

1, 1, 3, 4, 3, -15, -118, -336, -595, 1467, 20391, 96205, 353686, 574786, -2717256, -30598208, -197828371, -841728699, -2599029153, -1309899955, 56975269295, 522707807733, 3425068059553, 16747743739845, 63468629516172, 111911654532374, -907903172853988, -12555837715110897

Offset: 0

Author

Seiichi Manyama, Jun 15 2025

Keywords

• sign

Crossrefs

Column k=1 of A385018.

Cf. A384951, A385015, A385016.

Cf. A001764, A213228, A213229, A213230, A384974.

Cf. A384894.

Programs

PARI

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

Formula

See A385018.