A384898 G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x)^3)^3.

1, 1, 3, 6, 10, -39, -546, -3563, -18918, -68472, -47978, 2060310, 25856241, 210422728, 1367033271, 6837535155, 18339297562, -114989342976, -2525856651999, -27658429475813, -235591084478085, -1658029364805855, -9188248947018893, -28582654956147315, 177119046663378954

Offset: 0

Author

Seiichi Manyama, Jun 12 2025

Keywords

• sign

Crossrefs

Column k=1 of A384903.

Cf. A001764, A213096, A384896, A384897.

Programs

PARI

a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-3*n+4*j+k-1, j-1)*a(n-j, 3*j)/j));

Formula

See A384903.