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 A322441 #13 Jan 02 2021 10:35:19
%S A322441 1,0,0,0,6,60,630,9660,192906
%N A322441 Number of pairs of set partitions of {1,...,n} where no block of one is a subset or equal to any block of the other.
%C A322441 For any pair (X,Y) meeting the requirement, so does the pair (Y,X) which must be distinct from (X,Y), except for X = Y = {} when n = 0. Therefore all a(n) are even for n > 0. - _M. F. Hasler_, Dec 30 2020
%e A322441 The a(4) = 6 pairs of set partitions:
%e A322441 {{1,2},{3,4}} and {{1,3},{2,4}},
%e A322441 {{1,2},{3,4}} and {{1,4},{2,3}},
%e A322441 {{1,3},{2,4}} and {{1,2},{3,4}},
%e A322441 {{1,3},{2,4}} and {{1,4},{2,3}},
%e A322441 {{1,4},{2,3}} and {{1,2},{3,4}},
%e A322441 {{1,4},{2,3}} and {{1,3},{2,4}}.
%t A322441 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A322441 stabQ[u_]:=stabQ[u,SubsetQ];stabQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A322441 Table[Length[Select[Tuples[sps[Range[n]],2],And[UnsameQ@@Join@@#,stabQ[Join@@#]]&]],{n,6}]
%Y A322441 Cf. A000110, A000258, A001247, A008277, A059849, A060639, A181939, A318393, A321760 (unlabeled version), A322435, A322442.
%K A322441 nonn,more
%O A322441 0,5
%A A322441 _Gus Wiseman_, Dec 08 2018