

A048617


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


5



2, 2, 8, 72, 1152, 28800, 1036800, 50803200, 3251404800, 263363788800, 26336378880000, 3186701844480000, 458885065605120000, 77551576087265280000, 15200108913103994880000, 3420024505448398848000000, 875526273394790105088000000, 253027093011094340370432000000
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



