A375607 Expansion of e.g.f. 1 / (exp(-x^3) - x).

1, 1, 2, 12, 72, 480, 3960, 40320, 463680, 5866560, 82857600, 1297296000, 22133865600, 407869862400, 8096683795200, 172405968134400, 3915525770956800, 94443904345190400, 2412049832704512000, 65035187612185190400, 1845812342328514560000

Offset: 0

Author

Seiichi Manyama, Aug 21 2024

Keywords

• nonn

Crossrefs

Cf. A072597, A375604.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^3)-x)))

PARI

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

Formula

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

a(n) ~ sqrt(2*Pi) * 3^((n+1)/3) * n^(n + 1/2) / ((1 + LambertW(3)) * exp(n) * LambertW(3)^((n+1)/3)). - Vaclav Kotesovec, Aug 21 2024