A367392 a(n) = Sum_{k=0..n} (-1)^k * binomial(n, k) * (n - k)^(2*n + 1).

0, 1, 30, 1806, 186480, 29607600, 6711344640, 2060056318320, 823172919528960, 415357755774998400, 258323865658578720000, 194165346649139268480000, 173524374976148227519488000, 181871966450361851863879680000, 220951172052769326900328396800000

Offset: 0

Author

Peter Luschny, Nov 21 2023

Keywords

• nonn

Crossrefs

Cf. A000142, A048993, A131689, A247238.

Programs

Maple

a := n -> n! * Stirling2(2*n + 1, n):
seq(a(n), n = 0..14);

Mathematica

A367392[n_]:=n!StirlingS2[2n+1,n];
Array[A367392,20,0] (* Paolo Xausa, Nov 24 2023 *)

Formula

a(n) = n! * Stirling2(2*n + 1, n) = A000142(n) * A247238(n).