%I #9 Aug 11 2019 12:23:39
%S 1,1,5,71,4223,2725521,151914530499,28175294344381108057
%N Number of set-systems with {} that are closed under intersection and cover n vertices.
%F Inverse binomial transform of A102895. - _Andrew Howroyd_, Aug 10 2019
%e The a(2) = 5 set-systems:
%e {{},{1,2}}
%e {{},{1},{2}}
%e {{},{1},{1,2}}
%e {{},{2},{1,2}}
%e {{},{1},{2},{1,2}}
%t Table[Length[Select[Subsets[Subsets[Range[n]]],MemberQ[#,{}]&&Union@@#==Range[n]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]
%Y The case also closed under union is A000798.
%Y The connected case (i.e., with maximum) is A102894.
%Y The same for union instead of intersection is (also) A102894.
%Y The non-covering case is A102895.
%Y The BII-numbers of these set-systems (without the empty set) are A326880.
%Y The unlabeled case is A326883.
%Y Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Jul 30 2019
%E a(5)-a(7) from _Andrew Howroyd_, Aug 10 2019