A326372 Number of intersecting antichains of (possibly empty) subsets of {1..n}.

2, 3, 5, 13, 82, 2647, 1422565, 229809982113, 423295099074735261881

Offset: 0

Author

Gus Wiseman, Jul 01 2019

Keywords

• nonn
• more

Comments

A set system (set of sets) is an antichain if no edge is a subset of any other, and is intersecting if no two edges are disjoint.

Examples

			The a(0) = 2 through a(3) = 13 antichains:
  {}    {}     {}       {}
  {{}}  {{}}   {{}}     {{}}
        {{1}}  {{1}}    {{1}}
               {{2}}    {{2}}
               {{1,2}}  {{3}}
                        {{1,2}}
                        {{1,3}}
                        {{2,3}}
                        {{1,2,3}}
                        {{1,2},{1,3}}
                        {{1,2},{2,3}}
                        {{1,3},{2,3}}
                        {{1,2},{1,3},{2,3}}
		

Crossrefs

The case without empty edges is A001206.

The inverse binomial transform is the spanning case A305844.

The unlabeled case is A306007.

Maximal intersecting antichains are A326363.

Intersecting set systems are A051185.

Cf. A000372, A007363, A014466, A305843, A326361, A326362.

Formula

a(n) = A001206(n + 1) + 1.