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A326964
Number of connected set-systems covering a subset of {1..n}.
7
1, 2, 7, 112, 32253, 2147316942, 9223372023968335715, 170141183460469231667123699322514272668, 5789604461865809771178549250434395393752402807429031284280914691514037561273
OFFSET
0,2
COMMENTS
A set-system is a finite set of finite nonempty sets.
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.
Sequence in context: A000157 A264999 A326940 * A034902 A101429 A270749
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 10 2019
STATUS
approved