This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326881 #9 Aug 11 2019 12:23:39
%S A326881 1,1,5,71,4223,2725521,151914530499,28175294344381108057
%N A326881 Number of set-systems with {} that are closed under intersection and cover n vertices.
%F A326881 Inverse binomial transform of A102895. - _Andrew Howroyd_, Aug 10 2019
%e A326881 The a(2) = 5 set-systems:
%e A326881 {{},{1,2}}
%e A326881 {{},{1},{2}}
%e A326881 {{},{1},{1,2}}
%e A326881 {{},{2},{1,2}}
%e A326881 {{},{1},{2},{1,2}}
%t A326881 Table[Length[Select[Subsets[Subsets[Range[n]]],MemberQ[#,{}]&&Union@@#==Range[n]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]
%Y A326881 The case also closed under union is A000798.
%Y A326881 The connected case (i.e., with maximum) is A102894.
%Y A326881 The same for union instead of intersection is (also) A102894.
%Y A326881 The non-covering case is A102895.
%Y A326881 The BII-numbers of these set-systems (without the empty set) are A326880.
%Y A326881 The unlabeled case is A326883.
%Y A326881 Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878.
%K A326881 nonn,more
%O A326881 0,3
%A A326881 _Gus Wiseman_, Jul 30 2019
%E A326881 a(5)-a(7) from _Andrew Howroyd_, Aug 10 2019