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 A326570 #9 Aug 14 2019 01:48:51
%S A326570 2,1,1,4,17,186,3292,139161,14224121
%N A326570 Number of covering antichains of subsets of {1..n} with different edge-sizes.
%C A326570 An antichain is a finite set of finite sets, none of which is a subset of any other. It is covering if its union is {1..n}. The edge-sizes are the numbers of vertices in each edge, so for example the edge-sizes of {{1,3},{2,5},{3,4,5}} are {2,2,3}.
%e A326570 The a(0) = 2 through a(4) = 17 antichains:
%e A326570 {} {{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}}
%e A326570 {{}} {{1},{2,3}} {{1},{2,3,4}}
%e A326570 {{2},{1,3}} {{2},{1,3,4}}
%e A326570 {{3},{1,2}} {{3},{1,2,4}}
%e A326570 {{4},{1,2,3}}
%e A326570 {{1,2},{1,3,4}}
%e A326570 {{1,2},{2,3,4}}
%e A326570 {{1,3},{1,2,4}}
%e A326570 {{1,3},{2,3,4}}
%e A326570 {{1,4},{1,2,3}}
%e A326570 {{1,4},{2,3,4}}
%e A326570 {{2,3},{1,2,4}}
%e A326570 {{2,3},{1,3,4}}
%e A326570 {{2,4},{1,2,3}}
%e A326570 {{2,4},{1,3,4}}
%e A326570 {{3,4},{1,2,3}}
%e A326570 {{3,4},{1,2,4}}
%t A326570 stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];
%t A326570 cleq[n_]:=Select[stableSets[Subsets[Range[n]],SubsetQ[#1,#2]||Length[#1]==Length[#2]&],Union@@#==Range[n]&];
%t A326570 Table[Length[cleq[n]],{n,0,6}]
%Y A326570 Antichain covers are A006126.
%Y A326570 Set partitions with different block sizes are A007837.
%Y A326570 The case without singletons is A326569.
%Y A326570 (Antichain) covers with equal edge-sizes are A306021.
%Y A326570 Cf. A000372, A003182, A307249, A326026, A326514, A326566, A326572.
%K A326570 nonn,more
%O A326570 0,1
%A A326570 _Gus Wiseman_, Jul 18 2019
%E A326570 a(8) from _Andrew Howroyd_, Aug 13 2019