A379871 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^3) + x*A(x)^3.

1, 0, 1, -1, 37, -151, 5041, -45277, 1548457, -23466079, 857700181, -18904086037, 752753527021, -21985835786383, 961877988836857, -34996151990315341, 1686330291491184337, -73237182836313686719, 3882675760305075969949, -195288563442324161608165

Offset: 0

Author

Seiichi Manyama, Jan 05 2025

Keywords

• sign

Crossrefs

Cf. A379876, A379877, A379878.

Cf. A108919, A379868.

Programs

PARI

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

Formula

E.g.f.: ( (1/x) * Series_Reversion( x / (exp(-x) + x)^3 ) )^(1/3).

a(n) = -n! * Sum_{k=0..n} (-3*n+k-1)^(n-k-1) * binomial(3*n,k)/(n-k)!.