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%I #32 Jun 20 2022 06:37:27
%S 1,5,181,20381,4940101,2230319165,1692864345061,1997649164976701,
%T 3461226344139932101,8430034728440212411325,
%U 27875832970537774479832741,121651171242426267003975420221,684351364639262056751911086836101,4865203490721997132612204548628407485
%N 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.
%H N. J. Calkin, B. Novick and H. Ushijima-Mwesigwa, <a href="http://arxiv.org/abs/1506.00699">What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments</a>, arXiv:1506.00699 [math.CO], 2015.
%F 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).
%o (PARI) a(n)=sum(k=1,n, (stirling(n,k,2)*k!)^3/k) \\ _Charles R Greathouse IV_, Jun 03 2015
%Y Cf. A000629, A000670, A048993, A092552, A242280.
%K nonn
%O 1,2
%A _Hayato Ushijima-Mwesigwa_, Jun 03 2015
%E Offset changed to 1 by _Georg Fischer_, Jun 20 2022
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