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 A330628 #8 Feb 28 2020 13:01:31
%S A330628 1,1,1,5,42,423,5458,80926
%N A330628 Number of series/singleton-reduced rooted trees on strongly normal multisets of size n whose leaves are sets (not necessarily disjoint).
%C A330628 A series/singleton-reduced rooted tree on a multiset m is either the multiset m itself or a sequence of series/singleton-reduced rooted trees, one on each part of a multiset partition of m that is neither minimal (all singletons) nor maximal (only one part).
%C A330628 A finite multiset is strongly normal if it covers an initial interval of positive integers with weakly decreasing multiplicities.
%e A330628 The a(4) = 42 trees:
%e A330628 {{1}{1}{12}} {{12}{12}} {{1}{123}} {1234}
%e A330628 {{1}{{1}{12}}} {{1}{2}{12}} {{12}{13}} {{1}{234}}
%e A330628 {{1}{{2}{12}}} {{1}{1}{23}} {{12}{34}}
%e A330628 {{2}{{1}{12}}} {{1}{2}{13}} {{13}{24}}
%e A330628 {{1}{3}{12}} {{14}{23}}
%e A330628 {{1}{{1}{23}}} {{2}{134}}
%e A330628 {{1}{{2}{13}}} {{3}{124}}
%e A330628 {{1}{{3}{12}}} {{4}{123}}
%e A330628 {{2}{{1}{13}}} {{1}{2}{34}}
%e A330628 {{3}{{1}{12}}} {{1}{3}{24}}
%e A330628 {{1}{4}{23}}
%e A330628 {{2}{3}{14}}
%e A330628 {{2}{4}{13}}
%e A330628 {{3}{4}{12}}
%e A330628 {{1}{{2}{34}}}
%e A330628 {{1}{{3}{24}}}
%e A330628 {{1}{{4}{23}}}
%e A330628 {{2}{{1}{34}}}
%e A330628 {{2}{{3}{14}}}
%e A330628 {{2}{{4}{13}}}
%e A330628 {{3}{{1}{24}}}
%e A330628 {{3}{{2}{14}}}
%e A330628 {{3}{{4}{12}}}
%e A330628 {{4}{{1}{23}}}
%e A330628 {{4}{{2}{13}}}
%e A330628 {{4}{{3}{12}}}
%t A330628 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A330628 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A330628 strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];
%t A330628 ssrtrees[m_]:=Prepend[Join@@Table[Tuples[ssrtrees/@p],{p,Select[mps[m],Length[m]>Length[#1]>1&]}],m];
%t A330628 Table[Sum[Length[Select[ssrtrees[s],FreeQ[#,{___,x_Integer,x_Integer,___}]&]],{s,strnorm[n]}],{n,0,5}]
%Y A330628 The generalization where leaves are multisets is A330471.
%Y A330628 The non-singleton-reduced version is A330625.
%Y A330628 The unlabeled version is A330626.
%Y A330628 The case with all atoms distinct is A000311.
%Y A330628 Strongly normal multiset partitions are A035310.
%Y A330628 Cf. A000669, A004111, A004114, A005804, A196545, A281118, A330465, A330467, A330624, A330654, A330668.
%K A330628 nonn,more
%O A330628 0,4
%A A330628 _Gus Wiseman_, Dec 26 2019