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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 13 2019
STATUS
approved