A319291 Number of series-reduced locally disjoint rooted trees with n leaves spanning an initial interval of positive integers.
1, 2, 12, 107, 1299, 20764, 412957, 9817743
Offset: 1
Examples
The a(3) = 12 series-reduced locally disjoint rooted trees: (1(11)) (111) (1(22)) (2(12)) (122) (1(12)) (2(11)) (112) (1(23)) (2(13)) (3(12)) (123) The trees counted by A316651(4) but not by a(4): ((11)(12)) ((12)(13)) ((12)(22)) ((12)(23)) ((13)(23))
Crossrefs
Programs
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Mathematica
disjointQ[u_]:=Apply[And,Outer[#1==#2||Intersection[#1,#2]=={}&,u,u,1],{0,1}]; sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; gro[m_]:=gro[m]=If[Length[m]==1,{m},Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m],Length[#]>1&])],disjointQ]]; allnorm[n_Integer]:=Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1]; Table[Sum[Length[gro[m]],{m,allnorm[n]}],{n,5}]