%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