A385015 G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x))^3.

1, 1, 4, 4, -13, -81, -389, -198, 7455, 44515, 198661, 70243, -5428624, -40239313, -218619844, -408542577, 3648305171, 44441073999, 339489511573, 1430556904456, 2122222427956, -35048613488679, -504238969376070, -3684488832562182, -21342732340391295, -67688326964892247

Offset: 0

Author

Seiichi Manyama, Jun 15 2025

Keywords

• sign

Crossrefs

Column k=1 of A385019.

Cf. A384951, A385014, A385016.

Cf. A213231, A213232, A384975.

Cf. A384896.

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, 3*j)/j));

Formula

See A385019.