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A326945
Number of T_0 sets of subsets of {1..n} that are closed under intersection.
8
2, 4, 12, 96, 4404, 2725942, 151906396568, 28175293281055562650
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
The non-T_0 version is A102897.
The version not closed under intersection is A326941.
The covering case is A326943.
The case without empty edges is A326959.
Sequence in context: A120618 A259048 A228809 * A309718 A230814 A325502
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 08 2019
EXTENSIONS
a(5)-a(7) from Andrew Howroyd, Aug 14 2019
STATUS
approved