A381326 - OEIS

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

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OFFSET

1,1

LINKS

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

El-Mehdi Mehiri, Bijections Between Smirnov Words and Hamiltonian Cycles in Complete Multipartite Graphs, arXiv:2510.26597 [math.CO], 2025. See p. 10. Table 2.

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