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

0,1

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

Table of n, a(n) for n=0..17.

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

Formula

a(n) = 2*A001044(n)

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 *)

Prog

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

Crossrefs

Equals 2 * A001044.

Sequence in context: A003181 A009616 A005615 * A000615 A297010 A012413

Adjacent sequences: A048614 A048615 A048616 * A048618 A048619 A048620

Keyword

nonn

Author

N. J. A. Sloane

Status

approved