

A326964


Number of connected setsystems covering a subset of {1..n}.


1



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

0,2


COMMENTS

A setsystem is a finite set of finite nonempty sets.


LINKS



FORMULA



EXAMPLE

The a(0) = 1 through a(2) = 7 setsystems:
{} {} {}
{{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.
The BIInumbers of connected setsystems are A326749.


KEYWORD

nonn


AUTHOR



STATUS

approved



