A385366 a(n) = Sum_{permutations p of [n]} des(p^2), where des(p) is the number of descents of p.

0, 0, 2, 24, 192, 1560, 13680, 131040, 1370880, 15603840, 192326400, 2554675200, 36404121600, 554204851200, 8979363993600, 154305575424000, 2803653844992000, 53708801642496000, 1082001156268032000, 22869278876860416000, 506043617700741120000, 11699825757321461760000

Offset: 1

Author

Yifan Xie, Jun 26 2025

Keywords

• nonn
• easy

Examples

			For the permutation p = (2, 3, 4, 1), p^2 = (3, 4, 1, 2), and des(p) = des(p^2) = 1 (because 4 > 1).
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..445

Crossrefs

Cf. A001286.

Programs

Mathematica

A385366[n_] := If[n <= 2, 0, (n - 1)!*(n^2 - n - 4)/2];
Array[A385366, 25] (* Paolo Xausa, Jul 14 2025 *)

PARI

a(n)=if(n>2,(n-1)!*(n^2-n-4)/2, 0);

Formula

a(n) = 0 if n <= 2; a(n) = (n-1)!*(n^2-n-4)/2 if n >= 3.