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%I A326204 #13 Jul 23 2019 04:25:16
%S A326204 0,2,4,120,19104
%N A326204 Number of Hamiltonian labeled n-vertex digraphs (with loops).
%C A326204 A digraph is Hamiltonian if it contains a directed cycle passing through every vertex exactly once.
%H A326204 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%e A326204 The a(2) = 4 digraph edge-sets:
%e A326204 {12,21}
%e A326204 {11,12,21}
%e A326204 {12,21,22}
%e A326204 {11,12,21,22}
%t A326204 Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianCycle[Graph[Range[n],DirectedEdge@@@#]]!={}&]],{n,0,4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 19200 which is incorrect *)
%Y A326204 The unlabeled case is A326226.
%Y A326204 The case without loops is A326219.
%Y A326204 The undirected case (without loops) is A326208.
%Y A326204 Non-Hamiltonian digraphs are A326220.
%Y A326204 Digraphs containing a Hamiltonian path are A326214.
%Y A326204 Cf. A000595, A002416, A003024, A003216, A057864.
%K A326204 nonn,more
%O A326204 0,2
%A A326204 _Gus Wiseman_, Jun 14 2019