A234365 Number of directed Hamiltonian cycles in the complete tripartite graph K_{n,n,n}.

2, 32, 3168, 926208, 598579200, 723105792000, 1464887918592000, 4610898301943808000, 21308780838537658368000, 138404291567096011161600000, 1220304754650628950589440000000, 14197926030549494380143575040000000, 212919452788134597593544586690560000000, 4034887005978635554837074343530332160000000

Offset: 1

Author

Max Alekseyev, Dec 25 2013

Keywords

• nonn

Links

• Zlatko Damijanic, Table of n, a(n) for n = 1..160
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph.
• Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

Crossrefs

Cf. A000172, A141147, A307924.

Programs

Mathematica

Table[n!^2 (n - 1)! 2^n HypergeometricPFQ[{n, (1 - n)/2, -n/2}, {1, 1}, 1], {n, 10}] (* Eric W. Weisstein, Apr 26 2017 *)

Formula

a(n) = n!^2 * (n-1)! * A141147(n) = n!^2 * (n-1)! * (A000172(n-1)+A000172(n)) * 2 / 3.

a(n) = 2*A307924(n). - Andrew Howroyd, Nov 10 2024