A326951 Number of unlabeled sets of subsets of {1..n} where every covered vertex is the unique common element of some subset of the edges.

2, 4, 8, 40, 2464

Offset: 0

Author

Gus Wiseman, Aug 13 2019

Keywords

• nonn
• more

Comments

Alternatively, these are unlabeled sets of subsets of {1..n} whose dual is a (strict) antichain, also called T_1 sets of subsets. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. An antichain is a set of subsets where no edge is a subset of any other.

Examples

			Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:
  {}    {}        {}
  {{}}  {{}}      {{}}
        {{1}}     {{1}}
        {{},{1}}  {{},{1}}
                  {{1},{2}}
                  {{},{1},{2}}
                  {{1},{2},{1,2}}
                  {{},{1},{2},{1,2}}
		

Crossrefs

Unlabeled sets of subsets are A003180.

Unlabeled T_0 sets of subsets are A326949.

The labeled version is A326967.

The case without empty edges is A326972.

The covering case is A327011 (first differences).

Cf. A003181, A059052, A326960, A326965, A326969, A326974, A326976.

Formula

a(n) = 2 * A326972(n).

a(n) = Sum_{k = 0..n} A327011(k).