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

1, 1, 1, 2, 22, 2133

Offset: 0

Author

Gus Wiseman, Sep 25 2018

Keywords

• nonn
• more

Comments

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}}.

Examples

			The a(4) = 22 antichain covers:
   {{1,2,3,4}}
   {{3,4},{1,2,3},{1,2,4}}
   {{2,4},{1,2,3},{1,3,4}}
   {{2,3},{1,2,4},{1,3,4}}
   {{1,4},{1,2,3},{2,3,4}}
   {{1,3},{1,2,4},{2,3,4}}
   {{1,2},{1,3,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4}}
   {{1,2},{1,4},{2,3},{3,4}}
   {{1,2},{1,3},{2,4},{3,4}}
   {{1,4},{2,4},{3,4},{1,2,3}}
   {{1,3},{2,3},{3,4},{1,2,4}}
   {{1,2},{2,3},{2,4},{1,3,4}}
   {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4}}
   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
		

Crossrefs

Cf. A006126, A007716, A007718, A049311, A056156, A059201, A283877, A316980, A316983, A318099, A319557, A319565, A319616-A319646, A300913.