A381326 Number of (undirected) Hamiltonian cycles in the complete 4-partite graph K_{n,n,n,n}.

3, 744, 1833840, 18872165376, 553245728256000, 37106744352952320000, 4936487939183251906560000, 1177983332748595472891904000000, 467912746454054494167896413962240000, 292026962339084784352431710907924480000000, 273498538086199515052362271809542396313600000000

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Eric Weisstein's World of Mathematics, Complete k-Partite Graph.

Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

Formula

a(n) = A378241(n)/2.

Mathematica

Table[(n!)^4 Expand[Hypergeometric1F1[1 - n, 2, x]^4 x^3] /. x^p_ :> p!, {n, 11}]/2

Crossrefs

Cf. A378241 (directed Hamiltonian cycles).

Sequence in context: A100407 A332173 A119264 * A307926 A172895 A259369

Adjacent sequences: A381321 A381322 A381323 * A381327 A381328 A381329

Keyword

nonn

Author

Eric W. Weisstein, Feb 20 2025

Status

approved