A326964 Number of connected set-systems covering a subset of {1..n}.

1, 2, 7, 112, 32253, 2147316942, 9223372023968335715, 170141183460469231667123699322514272668, 5789604461865809771178549250434395393752402807429031284280914691514037561273

Offset: 0

Author

Gus Wiseman, Aug 10 2019

Keywords

• nonn

Comments

A set-system is a finite set of finite nonempty sets.

Examples

			The a(0) = 1 through a(2) = 7 set-systems:
  {}    {}     {}
        {{1}}  {{1}}
               {{2}}
               {{1,2}}
               {{1},{1,2}}
               {{2},{1,2}}
               {{1},{2},{1,2}}
		

Crossrefs

Covering sets of subsets are A000371.

Connected graphs are A001187.

The unlabeled version is A309667.

The BII-numbers of connected set-systems are A326749.

The covering case is A323818.

Cf. A007718, A048143, A058891, A092918, A300913, A304716, A326866, A326948.

Programs

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]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Length[csm[#]]<=1&]],{n,0,4}]

Formula

Binomial transform of A323818.