A379935 E.g.f. A(x) satisfies A(x) = 1/( exp(-x) - x*A(x) )^2.

1, 4, 38, 674, 17744, 623362, 27480844, 1460031610, 90862627184, 6485745312098, 522469881832964, 46895105170999978, 4641403797239576392, 502226056825606487506, 58985555898802967473820, 7473459685930447455067418, 1016083115772085962460442336, 147559760656716707828287356610

Offset: 0

Author

Seiichi Manyama, Jan 06 2025

Keywords

• nonn

Crossrefs

Cf. A379864, A379886, A379933.

Programs

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379886.

a(n) = 2 * n! * Sum_{k=0..n} (3*n-3*k+2)^(k-1) * binomial(3*n-3*k+2,n-k)/k!.