A392820 Expansion of e.g.f. 1/(1 - x*(exp(x) - 1)^2).

1, 0, 0, 6, 24, 70, 900, 10514, 88368, 969966, 14565660, 210128842, 3101829192, 53657039462, 1011396628788, 19614301352130, 407298714601056, 9155878501901278, 216531181241189964, 5365383438167708858, 140625865483389408120, 3879395530456330528854

Offset

0,4

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (2*k)! * Stirling2(n-k,2*k)/(n-k)!.

Mathematica

Table[n!*Sum[(2*k)!*Abs[StirlingS2[n-k, 2*k]/(n-k)!], {k, 0, Floor[n/3]}], {n, 0, 23}] (* Vincenzo Librandi, Jan 25 2026 *)

Prog

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

Crossrefs

Column k=2 of A392817.

Sequence in context: A392973 A006528 A052749 * A392826 A392825 A392766

Adjacent sequences: A392817 A392818 A392819 * A392821 A392822 A392823

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 24 2026

Status

approved