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 A326350 #6 Jun 30 2019 06:51:00
%S A326350 1,0,1,4,23,157,1182
%N A326350 Number of non-nesting connected simple graphs with vertices {1..n}.
%C A326350 Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d.
%H A326350 Gus Wiseman, <a href="/A326350/a326350.png">The a(4) = 23 non-nesting connected simple graphs</a>.
%H A326350 Gus Wiseman, <a href="/A326350/a326350_1.png">The a(5) = 157 non-nesting connected simple graphs</a>.
%t A326350 csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A326350 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Union@@#==Range[n]&&Length[csm[#]]<=1&&!MatchQ[#,{___,{x_,y_},___,{z_,t_},___}/;x<z<t<y||z<x<y<t]&]],{n,0,5}]
%Y A326350 The inverse binomial transform is the non-covering case A326351.
%Y A326350 Connected simple graphs are A001349.
%Y A326350 Connected simple graphs with no crossing or nesting edges are A326294.
%Y A326350 Simple graphs without crossing or nesting edges are A326244.
%Y A326350 Cf. A006125, A054726, A117662, A136653.
%Y A326350 Cf. A324169, A326210, A326293, A326329, A326340.
%K A326350 nonn,more
%O A326350 0,4
%A A326350 _Gus Wiseman_, Jun 30 2019