
MATHEMATICA

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]]]]]]]]];
spanEdgeConn[vts_, eds_]:=Length[eds]Max@@Length/@Select[Subsets[eds], Union@@#!=vtsLength[csm[#]]!=1&];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], spanEdgeConn[Range[n], #]==2&]], {n, 0, 4}]


CROSSREFS

Column k = 2 of A327069.
BIInumbers of setsystems with spanning edgeconnectivity 2 are A327108.
The generalization to setsystems is A327130.
Cf. A006129, A327070, A327071, A327102, A327109, A327111, A327129, A327144.
Sequence in context: A218536 A338377 A211048 * A158728 A197406 A197428
Adjacent sequences: A327143 A327144 A327145 * A327147 A327148 A327149
