A326942 - OEIS

%I #7 Aug 18 2019 08:27:36

%S 2,2,6,58,3770

%N Number of unlabeled T_0 sets of subsets of {1..n} that cover all n vertices.

%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 * A319637(n).

%e Non-isomorphic representatives of the a(0) = 2 through a(2) = 6 sets of subsets:

%e   {}    {{1}}     {{1},{2}}

%e   {{}}  {{},{1}}  {{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 A003181.

%Y The case without empty edges is A319637.

%Y The labeled version is A326939.

%Y The non-covering version is A326949 (partial sums).

%Y Cf. A000371, A003180, A055621, A059201, A316978, A319559, A319564, A326907, A326941, A326943, A326946.

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Aug 07 2019