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 A326902 #13 Aug 11 2019 13:51:30
%S A326902 1,1,3,19,319,21881,16417973,1063459099837,225402359008808647339
%N A326902 Number of set-systems (without {}) covering n vertices that are closed under intersection.
%C A326902 A set-system is a finite set of finite nonempty sets, so no two edges of a set-system that is closed under intersection can be disjoint.
%F A326902 Inverse binomial transform of A326901. - _Andrew Howroyd_, Aug 10 2019
%e A326902 The a(0) = 1 through a(3) = 19 set-systems:
%e A326902 {} {{1}} {{1,2}} {{1,2,3}}
%e A326902 {{1},{1,2}} {{1},{1,2,3}}
%e A326902 {{2},{1,2}} {{2},{1,2,3}}
%e A326902 {{3},{1,2,3}}
%e A326902 {{1,2},{1,2,3}}
%e A326902 {{1,3},{1,2,3}}
%e A326902 {{2,3},{1,2,3}}
%e A326902 {{1},{1,2},{1,3}}
%e A326902 {{2},{1,2},{2,3}}
%e A326902 {{3},{1,3},{2,3}}
%e A326902 {{1},{1,2},{1,2,3}}
%e A326902 {{1},{1,3},{1,2,3}}
%e A326902 {{2},{1,2},{1,2,3}}
%e A326902 {{2},{2,3},{1,2,3}}
%e A326902 {{3},{1,3},{1,2,3}}
%e A326902 {{3},{2,3},{1,2,3}}
%e A326902 {{1},{1,2},{1,3},{1,2,3}}
%e A326902 {{2},{1,2},{2,3},{1,2,3}}
%e A326902 {{3},{1,3},{2,3},{1,2,3}}
%t A326902 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Union@@#==Range[n]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]
%Y A326902 The case closed under union and intersection is A006058.
%Y A326902 The case with union instead of intersection is A102894.
%Y A326902 The unlabeled version is A108800(n - 1).
%Y A326902 The non-covering case is A326901.
%Y A326902 The connected case is A326903.
%Y A326902 Cf. A000798, A001930, A102895, A102898, A182507, A326866, A326876, A326878, A326882, A326900, A326901, A326904.
%K A326902 nonn,more
%O A326902 0,3
%A A326902 _Gus Wiseman_, Aug 04 2019
%E A326902 a(5)-a(8) from _Andrew Howroyd_, Aug 10 2019