A392821 Expansion of e.g.f. 1/(1 - x*(exp(x) - 1)^3).

1, 0, 0, 0, 24, 180, 900, 3780, 54768, 1140804, 17418300, 210178980, 2650531752, 48188322468, 1088845392180, 23476458341700, 470217271305696, 9819332643164292, 238311010157746860, 6480147279898338660, 179681470452942804120, 4958223441469749869796

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (3*k)! * Stirling2(n-k,3*k)/(n-k)!.

Mathematica

Table[n!*Sum[(3*k)!*Abs[StirlingS2[n-k, 3*k]/(n-k)!], {k, 0, Floor[n/4]}], {n, 0, 23}] (* Vincenzo Librandi, Jan 25 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\4, (3*k)!*stirling(n-k, 3*k, 2)/(n-k)!);
(Magma) [Factorial(n)* &+[Factorial(3*k)*Abs(StirlingSecond(n-k, 3*k))/Factorial(n-k) : k in [0..Floor(n/4)] ] : n in [0..23] ]; // Vincenzo Librandi, Jan 25 2026

Crossrefs

Column k=3 of A392817.

Cf. A353774.

Sequence in context: A297522 A165187 A052761 * A392851 A371158 A371198

Adjacent sequences: A392818 A392819 A392820 * A392822 A392823 A392824

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 24 2026

Status

approved