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 A320330 #6 Oct 11 2018 10:10:17
%S A320330 1,1,3,5,13,25,50,100,195,366,707,1333,2440
%N A320330 Number of T_0 multiset partitions of integer partitions of n.
%C A320330 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 A320330 The a(1) = 1 through a(5) = 25 multiset partitions:
%e A320330 {{1}} {{2}} {{3}} {{4}} {{5}}
%e A320330 {{1,1}} {{1,1,1}} {{2,2}} {{1,1,3}}
%e A320330 {{1},{1}} {{1},{2}} {{1,1,2}} {{1,2,2}}
%e A320330 {{1},{1,1}} {{1},{3}} {{1},{4}}
%e A320330 {{1},{1},{1}} {{2},{2}} {{2},{3}}
%e A320330 {{1,1,1,1}} {{1,1,1,2}}
%e A320330 {{1},{1,2}} {{1},{1,3}}
%e A320330 {{2},{1,1}} {{1},{2,2}}
%e A320330 {{1},{1,1,1}} {{2},{1,2}}
%e A320330 {{1,1},{1,1}} {{3},{1,1}}
%e A320330 {{1},{1},{2}} {{1,1,1,1,1}}
%e A320330 {{1},{1},{1,1}} {{1},{1,1,2}}
%e A320330 {{1},{1},{1},{1}} {{1,1},{1,2}}
%e A320330 {{1},{1},{3}}
%e A320330 {{1},{2},{2}}
%e A320330 {{2},{1,1,1}}
%e A320330 {{1},{1,1,1,1}}
%e A320330 {{1,1},{1,1,1}}
%e A320330 {{1},{1},{1,2}}
%e A320330 {{1},{2},{1,1}}
%e A320330 {{1},{1},{1,1,1}}
%e A320330 {{1},{1,1},{1,1}}
%e A320330 {{1},{1},{1},{2}}
%e A320330 {{1},{1},{1},{1,1}}
%e A320330 {{1},{1},{1},{1},{1}}
%t A320330 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A320330 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A320330 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t A320330 Table[Length[Select[Join@@mps/@IntegerPartitions[n],UnsameQ@@dual[#]&]],{n,8}]
%Y A320330 Cf. A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A316983, A319066, A319312, A320328, A320331.
%K A320330 nonn,more
%O A320330 0,3
%A A320330 _Gus Wiseman_, Oct 11 2018