A384897 G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x)^2)^3.

1, 1, 3, 3, -8, -81, -462, -1140, 1662, 42210, 341922, 1588428, 3968106, -17035461, -330216303, -2645037192, -15366663001, -56099904270, 42126523152, 2923843607931, 33032055390075, 253102960693959, 1474460670302136, 5496172108115193, -8530990617203547

Offset: 0

Author

Seiichi Manyama, Jun 12 2025

Keywords

• sign

Crossrefs

Column k=1 of A384902.

Cf. A001764, A213096, A384896, A384898.

Programs

PARI

a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-2*n+3*j+k-1, j-1)*a(n-j, 3*j)/j));

Formula

See A384902.