This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326240 #4 Jun 17 2019 21:47:26
%S A326240 0,2,0,8,160,6976,644992
%N A326240 Number of Hamiltonian labeled n-vertex graphs with loops.
%C A326240 A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
%F A326240 a(n) = A326208(n) * 2^n.
%e A326240 The a(3) = 8 edge-sets:
%e A326240 {12,13,23} {11,12,13,23} {11,12,13,22,23} {11,12,13,22,23,33}
%e A326240 {12,13,22,23} {11,12,13,23,33}
%e A326240 {12,13,23,33} {12,13,22,23,33}
%t A326240 Table[Length[Select[Subsets[Select[Tuples[Range[n],2],OrderedQ]],FindHamiltonianCycle[Graph[Range[n],#]]!={}&]],{n,0,5}]
%Y A326240 The unlabeled case is A326215.
%Y A326240 The directed case is A326204 (with loops) or A326219 (without loops).
%Y A326240 The case without loops A326208.
%Y A326240 Graphs with loops not containing a Hamiltonian cycle are A326239.
%Y A326240 Cf. A000088, A003216, A006125, A057864, A283420.
%K A326240 nonn,more
%O A326240 0,2
%A A326240 _Gus Wiseman_, Jun 17 2019