login
Number of intersecting antichains of (possibly empty) subsets of {1..n}.
3

%I #8 Jul 02 2019 11:18:15

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

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

%C 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.

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

%e The a(0) = 2 through a(3) = 13 antichains:

%e {} {} {} {}

%e {{}} {{}} {{}} {{}}

%e {{1}} {{1}} {{1}}

%e {{2}} {{2}}

%e {{1,2}} {{3}}

%e {{1,2}}

%e {{1,3}}

%e {{2,3}}

%e {{1,2,3}}

%e {{1,2},{1,3}}

%e {{1,2},{2,3}}

%e {{1,3},{2,3}}

%e {{1,2},{1,3},{2,3}}

%Y The case without empty edges is A001206.

%Y The inverse binomial transform is the spanning case A305844.

%Y The unlabeled case is A306007.

%Y Maximal intersecting antichains are A326363.

%Y Intersecting set systems are A051185.

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

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Jul 01 2019