OFFSET
0,2
COMMENTS
A set-system is a finite set of finite nonempty sets. The dual of a set-system 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-system where no edge is a subset of any other. This sequence counts set-systems whose dual is a (strict) antichain, also called T_1 set-systems.
EXAMPLE
The a(0) = 1 through a(2) = 5 set-systems:
{} {} {}
{{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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 10 2019
STATUS
approved