login
Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily distinct) sets.
0

%I #6 Oct 26 2018 12:50:18

%S 1,1,2,6,40,2309

%N Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of (not necessarily 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 The a(3) = 6 antichain covers:

%e {{1,2,3}}

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

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

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

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

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

%Y Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 25 2018