# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a319286 Showing 1-1 of 1 %I A319286 #4 Sep 17 2018 08:34:40 %S A319286 1,2,9,67,573,6933,97147,1666999 %N A319286 Number of series-reduced locally disjoint rooted trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n. %C A319286 A rooted tree is series-reduced if every non-leaf node has at least two branches. It is locally disjoint if no branch overlaps any other branch of the same root. %e A319286 The a(3) = 9 trees: %e A319286 (1(11)) %e A319286 (111) %e A319286 (1(12)) %e A319286 (2(11)) %e A319286 (112) %e A319286 (1(23)) %e A319286 (2(13)) %e A319286 (3(12)) %e A319286 (123) %e A319286 Examples of rooted trees that are not locally disjoint are ((11)(12)) and ((12)(13)). %t A319286 disjointQ[u_]:=Apply[And,Outer[#1==#2||Intersection[#1,#2]=={}&,u,u,1],{0,1}]; %t A319286 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}]; %t A319286 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; %t A319286 gro[m_]:=gro[m]=If[Length[m]==1,{m},Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m],Length[#]>1&])],disjointQ]]; %t A319286 Table[Sum[Length[gro[m]],{m,Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n]}],{n,5}] %Y A319286 Cf. A000081, A007562, A316473, A316475, A316494, A316495, A316496, A316497. %K A319286 nonn,more %O A319286 1,2 %A A319286 _Gus Wiseman_, Sep 16 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE