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 A326030 #4 Jul 19 2019 07:51:02
%S A326030 2,3,6,19,132,3578,826949
%N A326030 Number of antichains of subsets of {1..n} with different edge-sums.
%C A326030 An antichain is a finite set of finite sets, none of which is a subset of any other. The edge-sums are the sums of vertices in each edge, so for example the edge sums of {{1,3},{2,5},{3,4,5}} are {4,7,12}.
%e A326030 The a(0) = 2 through a(3) = 19 antichains:
%e A326030 {} {} {} {}
%e A326030 {{}} {{}} {{}} {{}}
%e A326030 {{1}} {{1}} {{1}}
%e A326030 {{2}} {{2}}
%e A326030 {{1,2}} {{3}}
%e A326030 {{1},{2}} {{1,2}}
%e A326030 {{1,3}}
%e A326030 {{2,3}}
%e A326030 {{1},{2}}
%e A326030 {{1,2,3}}
%e A326030 {{1},{3}}
%e A326030 {{2},{3}}
%e A326030 {{1},{2,3}}
%e A326030 {{2},{1,3}}
%e A326030 {{1,2},{1,3}}
%e A326030 {{1,2},{2,3}}
%e A326030 {{1},{2},{3}}
%e A326030 {{1,3},{2,3}}
%e A326030 {{1,2},{1,3},{2,3}}
%t A326030 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 A326030 cleqset[set_]:=stableSets[Subsets[set],SubsetQ[#1,#2]||Total[#1]==Total[#2]&];
%t A326030 Table[Length[cleqset[Range[n]]],{n,0,5}]
%Y A326030 Set partitions with different block-sums are A275780.
%Y A326030 MM-numbers of multiset partitions with different part-sums are A326535.
%Y A326030 The covering case is A326572.
%Y A326030 Antichains with equal edge-sums are A326574.
%Y A326030 Cf. A000372, A003182, A006126, A321469, A326519, A326571, A326573.
%K A326030 nonn,more
%O A326030 0,1
%A A326030 _Gus Wiseman_, Jul 18 2019