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 A318393 #6 Sep 06 2018 15:38:14
%S A318393 1,1,2,1,1,6,3,8,6,1,1,14,7,48,36,6,56,44,12,1,1,30,15,200,150,25,560,
%T A318393 440,120,10,552,440,140,20,1,1,62,31,720,540,90,3640,2860,780,65,8280,
%U A318393 6600,2100,300,15,7202,5632,1920,340,30,1,1,126,63,2408,1806
%N A318393 Regular tetrangle where T(n,k,i) is the number of pairs of set partitions of {1,...,n} with meet of length k and join of length i.
%e A318393 The T(3,3,1) = 8 pairs of set partitions:
%e A318393 {{1},{2},{3}} {{1,2,3}}
%e A318393 {{1},{2,3}} {{1,2},{3}}
%e A318393 {{1},{2,3}} {{1,3},{2}}
%e A318393 {{1,2},{3}} {{1},{2,3}}
%e A318393 {{1,2},{3}} {{1,3},{2}}
%e A318393 {{1,3},{2}} {{1},{2,3}}
%e A318393 {{1,3},{2}} {{1,2},{3}}
%e A318393 {{1,2,3}} {{1},{2},{3}}
%e A318393 Tetrangle begins:
%e A318393 1 1 1 1 1
%e A318393 2 1 6 3 14 7 30 15
%e A318393 8 6 1 48 36 6 200 150 25
%e A318393 56 44 12 1 560 440 120 10
%e A318393 552 440 140 20 1
%t A318393 csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Union[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
%t A318393 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A318393 spmeet[a_,b_]:=DeleteCases[Union@@Outer[Intersection,a,b,1],{}];spmeet[a_,b_,c__]:=spmeet[spmeet[a,b],c];
%t A318393 Table[Length[Select[Tuples[sps[Range[n]],2],And[Length[spmeet@@#]==k,Length[csm[Union@@#]]==j]&]],{n,6},{k,n},{j,k}]
%Y A318393 Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318390, A318391, A318392.
%K A318393 nonn,tabf
%O A318393 1,3
%A A318393 _Gus Wiseman_, Aug 25 2018