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 A322065 #6 Nov 26 2018 17:04:26
%S A322065 1,1,1,11,525,146513
%N A322065 Number of ways to choose a stable partition of a connected antichain of sets spanning n vertices.
%C A322065 A stable partition of a hypergraph or set system is a set partition of the vertices where no non-singleton edge has all its vertices in the same block.
%e A322065 The a(3) = 11 stable partitions. The connected antichain is on top, and below is a list of all its stable partitions.
%e A322065 {1,2,3} {1,3}{2,3} {1,2}{2,3} {1,2}{1,3} {1,2}{1,3}{2,3}
%e A322065 -------- -------- -------- -------- --------
%e A322065 {{1},{2,3}} {{1,2},{3}} {{1,3},{2}} {{1},{2,3}} {{1},{2},{3}}
%e A322065 {{1,2},{3}} {{1},{2},{3}} {{1},{2},{3}} {{1},{2},{3}}
%e A322065 {{1,3},{2}}
%e A322065 {{1},{2},{3}}
%t A322065 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A322065 stableSets[u_,Q_]:=If[Length[u]===0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r===w||Q[r,w]||Q[w,r]],Q]]]];
%t A322065 csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Union[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A322065 Table[Sum[Length[Select[stableSets[Complement[Subsets[Range[n]],Union@@Subsets/@stn],SubsetQ],And[Union@@#==Range[n],Length[csm[#]]==1]&]],{stn,sps[Range[n]]}],{n,5}]
%Y A322065 Cf. A000110, A001187, A006125, A048143, A229048, A240936, A245883, A277203, A321911, A321979, A322063, A322064.
%K A322065 nonn,more
%O A322065 0,4
%A A322065 _Gus Wiseman_, Nov 25 2018