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%I #9 Aug 15 2019 15:29:52
%S 2,4,12,96,4404,2725942,151906396568,28175293281055562650
%N Number of T_0 sets of subsets of {1..n} that are closed under intersection.
%C 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).
%F Binomial transform of A326943.
%e The a(0) = 2 through a(2) = 12 sets of subsets:
%e {} {} {}
%e {{}} {{}} {{}}
%e {{1}} {{1}}
%e {{},{1}} {{2}}
%e {{},{1}}
%e {{},{2}}
%e {{1},{1,2}}
%e {{2},{1,2}}
%e {{},{1},{2}}
%e {{},{1},{1,2}}
%e {{},{2},{1,2}}
%e {{},{1},{2},{1,2}}
%t Table[Length[Select[Subsets[Subsets[Range[n]]],UnsameQ@@dual[#]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]
%Y The non-T_0 version is A102897.
%Y The version not closed under intersection is A326941.
%Y The covering case is A326943.
%Y The case without empty edges is A326959.
%Y Cf. A003180, A182507, A316978, A319564, A326906, A326939, A326940, A326944, A326947.
%K nonn,more
%O 0,1
%A _Gus Wiseman_, Aug 08 2019
%E a(5)-a(7) from _Andrew Howroyd_, Aug 14 2019
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