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 A326340 #6 Jun 30 2019 06:50:37
%S A326340 1,1,1,1,4,9,19,42
%N A326340 Number of maximal simple graphs with vertices {1..n} and no crossing or nesting edges.
%C A326340 Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d.
%H A326340 Gus Wiseman, <a href="/A326340/a326340.png">The a(6) = 19 maximal non-crossing non-nesting graphs</a>.
%t A326340 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326340 Table[Length[fasmax[Select[Subsets[Subsets[Range[n],{2}]],!MatchQ[#,{___,{x_,y_},___,{z_,t_},___}/;x<z<y<t||x<z<t<y]&]]],{n,0,5}]
%Y A326340 Covering graphs with no crossing or nesting edges are A326329.
%Y A326340 The case with only crossing edges forbidden is A000108 shifted right twice.
%Y A326340 Simple graphs without crossing or nesting edges are A326244.
%Y A326340 Connected graphs with no crossing or nesting edges are A326339.
%Y A326340 Cf. A006125, A007297, A054726, A117662, A136653.
%Y A326340 Cf. A324169, A324327, A324328, A326279, A326293.
%K A326340 nonn,more
%O A326340 0,5
%A A326340 _Gus Wiseman_, Jun 29 2019