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

1,2

Links

Table of n, a(n) for n=1..14.

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.

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).

Prog

(PARI) a(n)=sum(k=1, n, (stirling(n, k, 2)*k!)^3/k) \\ Charles R Greathouse IV, Jun 03 2015

Crossrefs

Cf. A000629, A000670, A048993, A092552, A242280.

Sequence in context: A050239 A218690 A345338 * A304277 A208403 A280797

Adjacent sequences: A256283 A256284 A256285 * A256287 A256288 A256289

Keyword

nonn

Author

Hayato Ushijima-Mwesigwa, Jun 03 2015

Extensions

Offset changed to 1 by Georg Fischer, Jun 20 2022

Status

approved