A319623 - OEIS

%I #7 Oct 26 2018 12:50:18

%S 1,1,0,1,15,1957

%N Number of connected antichain covers of n vertices by distinct sets whose dual is also an antichain of 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}}.

%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 15 antichain covers:

%e 1: {{1}}

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

%e 4: {{1,2},{1,3},{2,4},{3,4}}

%e    {{1,3},{1,4},{2,3},{2,4}}

%e    {{1,2},{1,4},{2,3},{3,4}}

%e    {{1,4},{2,4},{3,4},{1,2,3}}

%e    {{1,3},{2,3},{3,4},{1,2,4}}

%e    {{1,2},{2,3},{2,4},{1,3,4}}

%e    {{1,2},{1,3},{1,4},{2,3,4}}

%e    {{1,3},{1,4},{2,3},{2,4},{3,4}}

%e    {{1,2},{1,4},{2,3},{2,4},{3,4}}

%e    {{1,2},{1,3},{2,3},{2,4},{3,4}}

%e    {{1,2},{1,3},{1,4},{2,4},{3,4}}

%e    {{1,2},{1,3},{1,4},{2,3},{3,4}}

%e    {{1,2},{1,3},{1,4},{2,3},{2,4}}

%e    {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

%e    {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

%Y Cf. A006126, A007716, A007718, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319558, A319565, A319616-A319646, A300913.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Sep 25 2018