A234633 Numbers of directed Hamiltonian paths in the complete tripartite graph K_{n,n,n}.

6, 240, 37584, 15095808, 12420864000, 18233911296000, 43492335022080000, 157551157218115584000, 823642573772373884928000, 5970637844437187690496000000, 58120324656942369834270720000000, 739968068159742816891489484800000000

Offset: 1

Author

Eric W. Weisstein, Dec 28 2013

Keywords

• nonn

Links

• Zlatko Damijanic, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph.
• Eric Weisstein's World of Mathematics, Hamiltonian Path.

Crossrefs

Cf. A234365, A234616, A110706.

Programs

Mathematica

Table[2 n!^3 (Binomial[2 n + 1, n + 1] HypergeometricPFQ[{1 - n, 1 - n, 1/2 - n/2, -(n/2)}, {1, -(1/2) - n, -n}, 1] + (n - 1) Binomial[2 n, n + 1] HypergeometricPFQ[{1 - n, 2 - n, 1/2 - n/2, 1 - n/2}, {2, 1/2 - n, -n}, 1]), {n, 10}] (* Eric W. Weisstein, May 26 2017 *)

Formula

a(n) = n!^3 * A110706(n). - Andrew Howroyd, May 24 2017

Extensions

a(7)-a(12) from Andrew Howroyd, May 24 2017