A326949 - OEIS

%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