A319637 - OEIS

%I #8 Jul 13 2022 14:59:54

%S 1,1,3,29,1885,18658259

%N Number of non-isomorphic T_0-covers of n vertices by distinct sets.

%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},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict (no repeated elements).

%e Non-isomorphic representatives of the a(3) = 29 covers:

%e    {{1,3},{2,3}}

%e    {{1},{2},{3}}

%e    {{1},{3},{2,3}}

%e    {{2},{3},{1,2,3}}

%e    {{2},{1,3},{2,3}}

%e    {{3},{1,3},{2,3}}

%e    {{3},{2,3},{1,2,3}}

%e    {{1,2},{1,3},{2,3}}

%e    {{1},{2},{3},{2,3}}

%e    {{1,3},{2,3},{1,2,3}}

%e    {{1},{2},{3},{1,2,3}}

%e    {{1},{2},{1,3},{2,3}}

%e    {{2},{3},{1,3},{2,3}}

%e    {{1},{3},{2,3},{1,2,3}}

%e    {{2},{3},{2,3},{1,2,3}}

%e    {{3},{1,2},{1,3},{2,3}}

%e    {{2},{1,3},{2,3},{1,2,3}}

%e    {{3},{1,3},{2,3},{1,2,3}}

%e    {{1},{2},{3},{1,3},{2,3}}

%e    {{1,2},{1,3},{2,3},{1,2,3}}

%e    {{1},{2},{3},{2,3},{1,2,3}}

%e    {{2},{3},{1,2},{1,3},{2,3}}

%e    {{1},{2},{1,3},{2,3},{1,2,3}}

%e    {{2},{3},{1,3},{2,3},{1,2,3}}

%e    {{3},{1,2},{1,3},{2,3},{1,2,3}}

%e    {{1},{2},{3},{1,2},{1,3},{2,3}}

%e    {{1},{2},{3},{1,3},{2,3},{1,2,3}}

%e    {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

%e    {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

%Y Cf. A006126, A007716, A049311, A059201, A283877, A316980, A316983, A318099, A319558, A319559, A319616-A319646, A300913.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 25 2018

%E a(5) from _Max Alekseyev_, Jul 13 2022