A256286 Number of Hamiltonian cycles in a tournament on 3n vertices constructed by taking 3 copies of a transitive tournament on n vertices and placing each copy on a vertex of a directed 3-cycle, with all edges between the copies oriented in the direction of the cycle.
1, 5, 181, 20381, 4940101, 2230319165, 1692864345061, 1997649164976701, 3461226344139932101, 8430034728440212411325, 27875832970537774479832741, 121651171242426267003975420221, 684351364639262056751911086836101, 4865203490721997132612204548628407485
Offset: 1
Keywords
Links
- N. J. Calkin, B. Novick and H. Ushijima-Mwesigwa, What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments, arXiv:1506.00699 [math.CO], 2015.
Programs
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PARI
a(n)=sum(k=1,n, (stirling(n,k,2)*k!)^3/k) \\ Charles R Greathouse IV, Jun 03 2015
Formula
a(n) = Sum_{k=1..n} (S(n,k)*k!)^3/k, where S(n,k) is the Stirling number of the second kind (A048993, Stirling set numbers).
Extensions
Offset changed to 1 by Georg Fischer, Jun 20 2022