A048617 a(n) = 2*(n!)^2.

2, 2, 8, 72, 1152, 28800, 1036800, 50803200, 3251404800, 263363788800, 26336378880000, 3186701844480000, 458885065605120000, 77551576087265280000, 15200108913103994880000, 3420024505448398848000000, 875526273394790105088000000, 253027093011094340370432000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) = automorphism group order for the complete bipartite graph K_{n,n}. - Avi Peretz (njk(AT)netvision.net.il), Feb 21 2001

For n > 1, also the order of automorphism group for the n X n rook graph. - Eric W. Weisstein, Jun 20 2017

Also the number of (directed) Hamiltonian paths in K_{n,n}. - Eric W. Weisstein, Jul 15 2011

For n>=1, a(n) is the number of ways to arrange n men and n women in a line so that no two people of the same gender are adjacent. - Geoffrey Critzer, Aug 24 2013

Also the number of (directed) Hamiltonian paths in the (n+1)-barbell graph. - Eric W. Weisstein, Dec 16 2013

Links

• Eric Weisstein's World of Mathematics, Graph Automorphism
• Eric Weisstein's World of Mathematics, Barbell Graph
• Eric Weisstein's World of Mathematics, Complete Bipartite Graph
• Eric Weisstein's World of Mathematics, Hamiltonian Path
• Eric Weisstein's World of Mathematics, Rook Graph

Crossrefs

Equals 2 * A001044.

Programs

Magma

[2*Factorial(n)^2: n in [0..30]]; // Vincenzo Librandi, Feb 22 2016

Maple

seq(mul(n!*k!, k=1..2), n=0..17); # Zerinvary Lajos, Jul 01 2007

Mathematica

2(Range[0,20]!)^2 (* Harvey P. Dale, Jun 21 2011 *)
Table[2 (n!)^2, {n, 0, 20}] (* Vincenzo Librandi, Feb 22 2016 *)

Formula

a(n) = 2*A001044(n)