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 A320331 #5 Oct 11 2018 10:10:24
%S A320331 1,1,2,4,8,17,30,61,110,207,381,711,1250
%N A320331 Number of strict T_0 multiset partitions of integer partitions of n.
%C A320331 The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The T_0 condition means the dual is strict.
%e A320331 The a(1) = 1 through a(5) = 17 multiset partitions:
%e A320331 {{1}} {{2}} {{3}} {{4}} {{5}}
%e A320331 {{1,1}} {{1,1,1}} {{2,2}} {{1,1,3}}
%e A320331 {{1},{2}} {{1,1,2}} {{1,2,2}}
%e A320331 {{1},{1,1}} {{1},{3}} {{1},{4}}
%e A320331 {{1,1,1,1}} {{2},{3}}
%e A320331 {{1},{1,2}} {{1,1,1,2}}
%e A320331 {{2},{1,1}} {{1},{1,3}}
%e A320331 {{1},{1,1,1}} {{1},{2,2}}
%e A320331 {{2},{1,2}}
%e A320331 {{3},{1,1}}
%e A320331 {{1,1,1,1,1}}
%e A320331 {{1},{1,1,2}}
%e A320331 {{1,1},{1,2}}
%e A320331 {{2},{1,1,1}}
%e A320331 {{1},{1,1,1,1}}
%e A320331 {{1,1},{1,1,1}}
%e A320331 {{1},{2},{1,1}}
%t A320331 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A320331 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A320331 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t A320331 Table[Length[Select[Join@@mps/@IntegerPartitions[n],And[UnsameQ@@#,UnsameQ@@dual[#]]&]],{n,8}]
%Y A320331 Cf. A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A319066, A319312, A320328, A320330.
%K A320331 nonn,more
%O A320331 0,3
%A A320331 _Gus Wiseman_, Oct 11 2018