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

1,1

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.

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

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 *)

Crossrefs

Cf. A000172, A141147, A307924.

Sequence in context: A329928 A093584 A117259 * A068183 A166077 A053853

Adjacent sequences: A234362 A234363 A234364 * A234366 A234367 A234368

Keyword

nonn

Author

Max Alekseyev, Dec 25 2013

Status

approved