A327808 Number of unlabeled, disconnected, nonempty antichains of subsets of {1..n}.

0, 0, 1, 3, 9, 32, 233, 16578

Offset: 0

Author

Gus Wiseman, Sep 26 2019

Keywords

• nonn
• more

Comments

An antichain is a set of nonempty sets, none of which is a subset of any other. A singleton is considered to be connected.

Examples

			Non-isomorphic representatives of the a(2) = 1 through a(4) = 9 antichains:
   {{1},{2}}  {{1},{2}}      {{1},{2}}
              {{1},{2,3}}    {{1},{2,3}}
              {{1},{2},{3}}  {{1},{2},{3}}
                             {{1},{2,3,4}}
                             {{1,2},{3,4}}
                             {{1},{2},{3,4}}
                             {{1},{2},{3},{4}}
                             {{2},{1,3},{1,4}}
                             {{4},{1,2},{1,3},{2,3}}
		

Crossrefs

The labeled version is A327354 - 1.

The covering case is A327426.

Unlabeled antichains that are either not connected or not covering are A327437.

The version with empty antichains allowed is A327424.

Cf. A000372, A014466, A120338, A293606, A326704, A327062, A327355.

Formula

a(n) = A327424(n) - 1.