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%I #13 Oct 11 2023 22:22:28
%S 2,4,10,68,3838,37320356
%N Number of unlabeled T_0 sets of subsets of {1..n}.
%C 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}}. The T_0 condition means that the dual is strict (no repeated edges).
%F a(n) = 2 * A326946(n).
%e Non-isomorphic representatives of the a(0) = 2 through a(2) = 10 sets of sets:
%e {} {} {}
%e {{}} {{}} {{}}
%e {{1}} {{1}}
%e {{},{1}} {{},{1}}
%e {{1},{2}}
%e {{2},{1,2}}
%e {{},{1},{2}}
%e {{},{2},{1,2}}
%e {{1},{2},{1,2}}
%e {{},{1},{2},{1,2}}
%Y The non-T_0 version is A003180.
%Y The labeled version is A326941.
%Y The covering case is A326942 (first differences).
%Y The case without empty edges is A326946.
%Y Cf. A000371, A000612, A003181, A059052, A245567, A316978, A319559, A319564, A319637, A326939, A326940.
%K nonn,more
%O 0,1
%A _Gus Wiseman_, Aug 08 2019
%E a(5) from _Max Alekseyev_, Oct 11 2023
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