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 A326351 #4 Jun 30 2019 06:51:08
%S A326351 1,1,2,8,46,323,2565
%N A326351 Number of non-nesting connected simple graphs on a subset of {1..n}.
%C A326351 Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d.
%t A326351 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 A326351 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[csm[#]]<=1&&!MatchQ[#,{___,{x_,y_},___,{z_,t_},___}/;x<z<t<y||z<x<y<t]&]],{n,0,5}]
%Y A326351 The binomial transform is the covering case A326350.
%Y A326351 Connected simple graphs are A001349.
%Y A326351 Connected simple graphs with no crossing or nesting edges are A326294.
%Y A326351 Simple graphs without crossing or nesting edges are A326244.
%Y A326351 Cf. A006125, A054726, A117662, A136653.
%Y A326351 Cf. A324169, A326210, A326293, A326329, A326340.
%K A326351 nonn,more
%O A326351 0,3
%A A326351 _Gus Wiseman_, Jun 30 2019