OFFSET
0,1
COMMENTS
The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges).
FORMULA
Binomial transform of A326943.
EXAMPLE
The a(0) = 2 through a(2) = 12 sets of subsets:
{} {} {}
{{}} {{}} {{}}
{{1}} {{1}}
{{},{1}} {{2}}
{{},{1}}
{{},{2}}
{{1},{1,2}}
{{2},{1,2}}
{{},{1},{2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{},{1},{2},{1,2}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n]]], UnsameQ@@dual[#]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 08 2019
EXTENSIONS
a(5)-a(7) from Andrew Howroyd, Aug 14 2019
STATUS
approved