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%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
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