A319640 Number of non-isomorphic antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

1, 1, 1, 2, 7, 70

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

			Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 antichains:
1: {{1}}
2: {{1},{2}}
3: {{1},{2},{3}}
   {{1,2},{1,3},{2,3}}
4: {{1},{2},{3},{4}}
   {{1},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3,4}}
   {{1,2},{1,3},{2,4},{3,4}}
   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
   {{1,3},{1,4},{2,3},{2,4},{3,4}}
   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
		

Crossrefs

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