A384942 G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^5.

1, 1, 5, -5, -135, -110, 3661, 16440, -1375, -827075, -8388505, 2298072, 496514205, 2782147265, 322830120, -164675585390, -1846591014842, -3084367863270, 84920580735040, 845318162940805, 4163798547024100, -18708392155753220, -503209620889452990, -3212928238924865090

Offset: 0

Author

Seiichi Manyama, Jun 13 2025

Keywords

• sign

Crossrefs

Column k=1 of A384945.

Cf. A002294, A213104.

Cf. A000012, A384894, A384896, A384941, A384943.

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, 5*j)/j));

Formula

See A384945.