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 A320351 #5 Oct 12 2018 22:43:01
%S A320351 1,1,3,5,11,18,38,66,130,237,449,823,1538
%N A320351 Number of connected multiset partitions of integer partitions of n.
%e A320351 The a(1) = 1 through a(5) = 18 multiset partitions:
%e A320351 {{1}} {{2}} {{3}} {{4}} {{5}}
%e A320351 {{1,1}} {{1,2}} {{1,3}} {{1,4}}
%e A320351 {{1},{1}} {{1,1,1}} {{2,2}} {{2,3}}
%e A320351 {{1},{1,1}} {{1,1,2}} {{1,1,3}}
%e A320351 {{1},{1},{1}} {{2},{2}} {{1,2,2}}
%e A320351 {{1,1,1,1}} {{1,1,1,2}}
%e A320351 {{1},{1,2}} {{1},{1,3}}
%e A320351 {{1},{1,1,1}} {{2},{1,2}}
%e A320351 {{1,1},{1,1}} {{1,1,1,1,1}}
%e A320351 {{1},{1},{1,1}} {{1},{1,1,2}}
%e A320351 {{1},{1},{1},{1}} {{1,1},{1,2}}
%e A320351 {{1},{1,1,1,1}}
%e A320351 {{1,1},{1,1,1}}
%e A320351 {{1},{1},{1,2}}
%e A320351 {{1},{1},{1,1,1}}
%e A320351 {{1},{1,1},{1,1}}
%e A320351 {{1},{1},{1},{1,1}}
%e A320351 {{1},{1},{1},{1},{1}}
%t A320351 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A320351 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A320351 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 A320351 Table[Length[Select[Join@@mps/@IntegerPartitions[n],Length[csm[#]]==1&]],{n,8}]
%Y A320351 Cf. A001970, A007718, A048143, A056156, A258466, A261006, A293994, A319719, A320328, A320330, A320331, A320355, A320356.
%K A320351 nonn,more
%O A320351 0,3
%A A320351 _Gus Wiseman_, Oct 11 2018