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

1,3

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001286.

Sequence in context: A126190 A121356 A052780 * A245019 A189769 A208533

Adjacent sequences: A385363 A385364 A385365 * A385367 A385368 A385369

Keyword

nonn,easy

Author

Yifan Xie, Jun 26 2025

Status

approved