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A326960 Number of sets of subsets of {1..n} covering all n vertices whose dual is a (strict) antichain, also called covering T_1 sets of subsets. 9
2, 2, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Same as A059052 except with a(1) = 2 instead of 4.
The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of subsets where no edge is a subset of any other.
Alternatively, these are sets of subsets of {1..n} covering all n vertices where every vertex is the unique common element of some subset of the edges.
LINKS
FORMULA
Binomial transform of A326967.
EXAMPLE
The a(0) = 2 through a(2) = 4 sets of subsets:
{} {{1}} {{1},{2}}
{{}} {{},{1}} {{},{1},{2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Union[Select[Intersection@@@Rest[Subsets[#]], Length[#]==1&]]]==n&]], {n, 0, 3}]
CROSSREFS
Covering sets of subsets are A000371.
Covering T_0 sets of subsets are A326939.
The case without empty edges is A326961.
The non-covering version is A326967.
Sequence in context: A345758 A178981 A050923 * A067700 A270554 A037010
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 13 2019
STATUS
approved

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Last modified September 29 02:45 EDT 2023. Contains 365749 sequences. (Running on oeis4.)