A226283 a(n) = [n/2]!*[(n+1)/2]!*C([n/2],2)*C([(n+1)/2],2).

0, 0, 0, 4, 36, 324, 2592, 20736, 172800, 1440000, 12960000, 116640000, 1143072000, 11202105600, 119489126400, 1274550681600, 14748372172800, 170659735142400, 2133246689280000, 26665583616000000, 358503957504000000, 4819886539776000000, 69406366172774400000

Offset: 1

Author

R. H. Hardin, connection of formula with combinatoric problem via N. J. A. Sloane in the Sequence Fans Mailing List, Jun 02 2013

Keywords

• nonn

Comments

Number of permutations of n elements with 4 odd displacements.

Column 3 of A226288.

Column k=4 of A145893, a diagonal of A145894. - Alois P. Heinz, May 29 2014

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A145893, A145894, A226288.

Programs

Mathematica

a[n_]:=(Floor[n/2])!(Floor[(n+1)/2])!Binomial[Floor[n/2],2]Binomial[Floor[(n+1)/2],2]; Array[a,23] (* Stefano Spezia, Jul 12 2024 *)