login
Number of (directed) Hamiltonian cycles on the complete graph K_n.
1

%I #13 Oct 21 2018 13:45:41

%S 0,0,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,

%T 6227020800,87178291200,1307674368000,20922789888000,355687428096000,

%U 6402373705728000,121645100408832000,2432902008176640000

%N Number of (directed) Hamiltonian cycles on the complete graph K_n.

%C a(n) is also the number of (directed) Hamiltonian paths on the complete graph K_{n-1}.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteGraph.html">Complete Graph</a>, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>.

%F a(1) = 0, a(2) = 0, a(n) = (n-1)! = A104150(n) for n > 2. - _Georg Fischer_, Oct 21 2018

%Y Cf. A000142, A104150.

%K nonn

%O 1,3

%A _Eric W. Weisstein_, Nov 05 2006