A384951 G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x)).

1, 1, 2, 3, 5, 6, 2, -20, -102, -312, -795, -1483, -1102, 7035, 51059, 219453, 779078, 2307104, 5508377, 7633065, -19349069, -226127800, -1296826960, -5855601434, -22970901723, -78578482054, -224208769108, -429111559993, 429212740026, 10534398465308

Offset: 0

Author

Seiichi Manyama, Jun 14 2025

Keywords

• sign

Comments

Compare to: B(x) = 1 + x/B(-x*B(x)) holds when B(x) = 1/(1-x).

Crossrefs

Column k=1 of A384976.

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, j)/j));

Formula

See A384976.