

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.


6



2, 2, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584
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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

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


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 noncovering version is A326967.
Cf. A003181, A059052, A059523, A319639, A326951, A326965, A326974, A326976, A326977, A326979.
Sequence in context: A177956 A178981 A050923 * A067700 A270554 A037010
Adjacent sequences: A326957 A326958 A326959 * A326961 A326962 A326963


KEYWORD

nonn


AUTHOR

Gus Wiseman, Aug 13 2019


STATUS

approved



