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 A320355 #6 Oct 12 2018 22:43:13
%S A320355 1,1,3,4,8,9,19,24,45,71,118,194,335
%N A320355 Number of connected antichains of multisets whose multiset union is an integer partition of n.
%H A320355 Goran Kilibarda and Vladeta Jovovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Kilibarda/kili2.pdf">Antichains of Multisets</a>, Journal of Integer Sequences, Vol. 7 (2004).
%e A320355 The a(1) = 1 through a(5) = 9 clutters:
%e A320355 {{1}} {{2}} {{3}} {{4}} {{5}}
%e A320355 {{1,1}} {{1,2}} {{1,3}} {{1,4}}
%e A320355 {{1},{1}} {{1,1,1}} {{2,2}} {{2,3}}
%e A320355 {{1},{1},{1}} {{1,1,2}} {{1,1,3}}
%e A320355 {{2},{2}} {{1,2,2}}
%e A320355 {{1,1,1,1}} {{1,1,1,2}}
%e A320355 {{1,1},{1,1}} {{1,1,1,1,1}}
%e A320355 {{1},{1},{1},{1}} {{1,1},{1,2}}
%e A320355 {{1},{1},{1},{1},{1}}
%t A320355 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A320355 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A320355 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 A320355 submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]];
%t A320355 antiQ[s_]:=Select[Tuples[s,2],And[UnsameQ@@#,submultisetQ@@#]&]=={};
%t A320355 Table[Length[Select[Join@@mps/@IntegerPartitions[n],And[Length[csm[#]]==1,antiQ[#]]&]],{n,8}]
%Y A320355 Cf. A001970, A007718, A048143, A258466, A261006, A293994, A318403, A319079, A319719, A319721, A320330, A320351, A320353, A320356.
%K A320355 nonn,more
%O A320355 0,3
%A A320355 _Gus Wiseman_, Oct 11 2018