

A326965


Number of setsystems on n vertices where every covered vertex is the unique common element of some subset of the edges.


20



1, 2, 5, 46, 19181, 2010327182, 9219217424630040409, 170141181796805106025395618012972506978, 57896044618658097536026644159052312978532934306727333157337631572314050272137
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OFFSET

0,2


COMMENTS

A setsystem is a finite set of finite nonempty sets. The dual of a setsystem 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 setsystem where no edge is a subset of any other. This sequence counts setsystems whose dual is a (strict) antichain, also called T_1 setsystems.


LINKS

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


FORMULA

Binomial transform of A326961.
a(n) = A326967(n)/2.


EXAMPLE

The a(0) = 1 through a(2) = 5 setsystems:
{} {} {}
{{1}} {{1}}
{{2}}
{{1},{2}}
{{1},{2},{1,2}}


MATHEMATICA

tmQ[eds_]:=Union@@Select[Intersection@@@Rest[Subsets[eds]], Length[#]==1&]==Union@@eds;
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], tmQ]], {n, 0, 3}]


CROSSREFS

Setsystems are A058891.
T_0 setsystems are A326940.
The covering case is A326961.
The version with empty edges allowed is A326967.
Setsystems whose dual is a weak antichain are A326968.
The unlabeled version is A326972.
The BII_numbers of these setsystems are A326979.
Cf. A059052, A326951, A326966, A326970, A326971, A326976, A326977.
Sequence in context: A121621 A225147 A119715 * A023273 A041729 A078665
Adjacent sequences: A326962 A326963 A326964 * A326966 A326967 A326968


KEYWORD

nonn


AUTHOR

Gus Wiseman, Aug 10 2019


STATUS

approved



