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 A326213 #13 Jun 11 2024 15:37:41
%S A326213 1,2,4,128,12352,3826272,3775441536
%N A326213 Number of labeled n-vertex digraphs (with loops) not containing a (directed) Hamiltonian path.
%C A326213 A path is Hamiltonian if it passes through every vertex exactly once.
%H A326213 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%H A326213 Gus Wiseman, <a href="http://arxiv.org/abs/0709.0430">Enumeration of paths and cycles and e-coefficients of incomparability graphs</a>, arXiv:0709.0430 [math.CO], 2007.
%F A326213 A002416(n) = a(n) + A326214(n).
%t A326213 Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianPath[Graph[Range[n],DirectedEdge@@@#]]=={}&]],{n,0,3}] (* Mathematica 10.2+ *)
%Y A326213 The unlabeled case is A326224.
%Y A326213 The case without loops is A326216.
%Y A326213 Digraphs containing a Hamiltonian path are A326214.
%Y A326213 Digraphs not containing a Hamiltonian cycle are A326220.
%Y A326213 Cf. A000595, A002416, A003024, A003216, A057864, A283420, A326204, A326206, A326221.
%K A326213 nonn,more
%O A326213 0,2
%A A326213 _Gus Wiseman_, Jun 15 2019
%E A326213 a(5)-a(6) from _Bert Dobbelaere_, Jun 11 2024