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A326964
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Number of connected set-systems covering a subset of {1..n}.
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1
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1, 2, 7, 112, 32253, 2147316942, 9223372023968335715, 170141183460469231667123699322514272668, 5789604461865809771178549250434395393752402807429031284280914691514037561273
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OFFSET
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0,2
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COMMENTS
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A set-system is a finite set of finite nonempty sets.
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LINKS
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Table of n, a(n) for n=0..8.
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FORMULA
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Binomial transform of A323818.
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EXAMPLE
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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}}
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MATHEMATICA
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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}]
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Aug 10 2019
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STATUS
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approved
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