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

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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..8.

Formula

Binomial transform of A323818.

Example

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}}

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}]

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.

Sequence in context: A000157 A264999 A326940 * A034902 A101429 A270749

Adjacent sequences: A326961 A326962 A326963 * A326965 A326966 A326967

Keyword

nonn

Author

Gus Wiseman, Aug 10 2019

Status

approved