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%I #8 Aug 15 2019 15:38:56
%S 2,4,14,224,64210,4294322204,18446744009291513774,
%T 340282366920938463075992982725615419816,
%U 115792089237316195423570985008687907843742078391854287068939455414919611614210
%N Number of T_0 sets of subsets of {1..n}.
%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, counted with multiplicity. 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 a(n) = 2 * A326940(n).
%F Binomial transform of A326939.
%e The a(0) = 2 through a(2) = 14 sets of subsets:
%e {} {} {}
%e {{}} {{}} {{}}
%e {{1}} {{1}}
%e {{},{1}} {{2}}
%e {{},{1}}
%e {{},{2}}
%e {{1},{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}}
%e {{},{1},{2},{1,2}}
%t dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t Table[Length[Select[Subsets[Subsets[Range[n]]],UnsameQ@@dual[#]&]],{n,0,3}]
%Y The non-T_0 version is A001146.
%Y The covering case is A326939.
%Y The case without empty edges is A326940.
%Y The unlabeled version is A326949.
%Y Cf. A003180, A059201, A316978, A319559, A319564, A319637, A326946, A326947.
%K nonn
%O 0,1
%A _Gus Wiseman_, Aug 07 2019
%E a(5)-a(8) from _Andrew Howroyd_, Aug 14 2019
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