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 A319291 Number of series-reduced locally disjoint rooted trees with n leaves spanning an initial interval of positive integers. 0
 1, 2, 12, 107, 1299, 20764, 412957, 9817743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE 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)) 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}] CROSSREFS Cf. A000081, A007562, A301700, A316473, A316475, A316495, A316651, A316694, A316695, A316696, A316697, A319286. Sequence in context: A275765 A184975 A268538 * A265132 A080446 A301411 Adjacent sequences:  A319288 A319289 A319290 * A319292 A319293 A319294 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 16 2018 STATUS approved

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Last modified April 23 10:57 EDT 2021. Contains 343204 sequences. (Running on oeis4.)