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%I #9 Jun 21 2019 07:57:40
%S 0,1,0,1,10,218,10078,896756,151676112,47754337568,28229412456056,
%T 31665593711174080
%N Number of Hamiltonian labeled simple graphs with n vertices.
%C A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
%H F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 9766535.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%H Gus Wiseman, <a href="/A326208/a326208.png">The a(5) = 218 simple graphs containing a Hamiltonian cycle.</a>
%F A006125(n) = a(n) + A326207(n).
%t Table[Length[Select[Subsets[Subsets[Range[n],{2}]],FindHamiltonianCycle[Graph[Range[n],#]]!={}&]],{n,0,4}] (* Mathematica 8.0+ *)
%Y The unlabeled version is A003216.
%Y The directed version is A326204 (with loops) or A326219 (without loops).
%Y Simple graphs not containing a Hamiltonian cycle are A326207.
%Y Simple graphs containing a Hamiltonian path are A326206.
%Y Cf. A003216, A006125, A057864, A283420.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Jun 15 2019
%E a(7)-a(11) added using tinygraph by _Falk Hüffner_, Jun 21 2019
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