A391877 - OEIS

A391877

Number of directed Hamiltonian cycles in the complete 5-partite graph K_{n,n,n,n,n}.

24, 112512, 8730457344, 3965523677282304, 6602585886478172160000, 30755963063492987269939200000, 335936272110882930782166948249600000, 7595808835329828456450518426001290035200000, 324050343201501938055429125845935244614775603200000, 24278966939813101209237186604565422347654745030656000000000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..10.

Peter Horák and Leoš Továrek, On Hamiltonian cycles of complete n-partite graphs, Mathematica Slovaca, vol. 29 (1979), 43-47.

Medet Jumadildayev, Duality Relations of Graph Polynomials, arXiv:2512.15351 [math.CO], 2025.

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

Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

FORMULA

a(n) = Integral_{t=0..oo} (e^(-t)/t) * ((-1)^n * n! * LaguerreL(n, -1, t))^5 dt.

MATHEMATICA

With[{m := 5}, Table[Expand[((-1) ^ n n! LaguerreL[n, -1, t]) ^ m] /. t ^ n_ :> (n - 1)!, {n, 10}]]

CROSSREFS

Cf. A378241, A234365, A010790.

Sequence in context: A382620 A159388 A172628 * A294318 A061527 A210278

Adjacent sequences: A391874 A391875 A391876 * A391878 A391879 A391880

KEYWORD

nonn

AUTHOR

Medet Jumadildayev, Dec 21 2025

STATUS

approved