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 A318394 #8 Aug 29 2018 16:48:56
%S A318394 2,4,18,316,37492
%N A318394 Number of finite sets of set partitions of {1,...,n} such that any two have meet {{1},...,{n}}.
%e A318394 The a(3) = 18 sets of set partitions:
%e A318394 0
%e A318394 {{1,2,3}}
%e A318394 {{1,3},{2}}
%e A318394 {{1,2},{3}}
%e A318394 {{1},{2,3}}
%e A318394 {{1},{2},{3}}
%e A318394 {{1,2},{3}} {{1,3},{2}}
%e A318394 {{1},{2,3}} {{1,3},{2}}
%e A318394 {{1},{2,3}} {{1,2},{3}}
%e A318394 {{1},{2},{3}} {{1,2,3}}
%e A318394 {{1},{2},{3}} {{1,3},{2}}
%e A318394 {{1},{2},{3}} {{1,2},{3}}
%e A318394 {{1},{2},{3}} {{1},{2,3}}
%e A318394 {{1},{2,3}} {{1,2},{3}} {{1,3},{2}}
%e A318394 {{1},{2},{3}} {{1,2},{3}} {{1,3},{2}}
%e A318394 {{1},{2},{3}} {{1},{2,3}} {{1,3},{2}}
%e A318394 {{1},{2},{3}} {{1},{2,3}} {{1,2},{3}}
%e A318394 {{1},{2},{3}} {{1},{2,3}} {{1,2},{3}} {{1,3},{2}}
%t A318394 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 A318394 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A318394 spmeet[a_,b_]:=DeleteCases[Union@@Outer[Intersection,a,b,1],{}];spmeet[a_,b_,c__]:=spmeet[spmeet[a,b],c];
%t A318394 Table[Length[stableSets[sps[Range[n]],Max@@Length/@spmeet[#1,#2]>1&]],{n,5}]
%Y A318394 Cf. A000110, A000258, A008277, A059849, A060639, A096827, A181939.
%Y A318394 Cf. A318389, A318390, A318391, A318392, A318531, A318532, A318531, A318532.
%K A318394 nonn,more
%O A318394 1,1
%A A318394 _Gus Wiseman_, Aug 25 2018