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A319620 Number of connected antichain covers of n vertices by distinct sets whose dual is also a (not necessarily strict) antichain. 0

%I

%S 1,1,1,2,22,2133

%N Number of connected antichain covers of n vertices by distinct sets whose dual is also a (not necessarily strict) antichain.

%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(4) = 22 antichain covers:

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

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

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

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

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

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

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

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

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

%e {{1,2},{1,3},{2,4},{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, A049311, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Sep 25 2018

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Last modified April 21 13:48 EDT 2021. Contains 343154 sequences. (Running on oeis4.)