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 A327375 #4 Sep 09 2019 12:05:21
%S A327375 0,0,0,72,4752
%N A327375 Number of set-systems with n vertices and vertex-connectivity 2.
%C A327375 A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.
%t A327375 csm[s_]:=With[{c=Select[Subsets[Range[Length[s]],{2}],Length[Intersection@@s[[#]]]>0&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A327375 vertConnSys[vts_,eds_]:=Min@@Length/@Select[Subsets[vts],Function[del,Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds,Alternatives@@del,{2}],{}]]!={Complement[vts,del]}]];
%t A327375 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],vertConnSys[Range[n],#]==2&]],{n,0,3}]
%Y A327375 BII-numbers for vertex-connectivity 2 are A327374.
%Y A327375 BII-numbers for cut-connectivity 2 are A327082.
%Y A327375 BII-numbers for spanning edge-connectivity 2 are A327108.
%Y A327375 BII-numbers for non-spanning edge-connectivity 2 are A327097.
%Y A327375 Labeled graphs with vertex-connectivity 2 are A327198.
%Y A327375 The vertex-connectivity of the set-system with BII-number n is A327051(n).
%Y A327375 The enumeration of labeled graphs by vertex-connectivity is A327334.
%Y A327375 Cf. A013922, A259862, A322389, A322390, A323818, A327336.
%K A327375 nonn,more
%O A327375 0,4
%A A327375 _Gus Wiseman_, Sep 05 2019