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 A316697 Number of series-reduced locally disjoint rooted trees with n unlabeled leaves. 1
 1, 1, 2, 5, 10, 24, 49, 112, 241, 548, 1218, 2839, 6547, 15572, 37179, 90555, 222065, 552576, 1384820, 3506475, 8936121, 22941280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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 (unequal) branch of the same root. LINKS EXAMPLE The a(5) = 10 trees:   o(o(o(oo))))   (o(o(ooo)))   (o((oo)(oo)))   (o(oo(oo)))   (o(oooo))   (oo(o(oo)))   (oo(ooo))   (o(oo)(oo))   (ooo(oo))   (ooooo) Missing from this list but counted by A000669 are ((oo)(o(oo))) and ((oo)(ooo)). MATHEMATICA disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}]; nms[n_]:=nms[n]=If[n==1, {{1}}, Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], disjointQ], {ptn, Rest[IntegerPartitions[n]]}]]; Table[Length[nms[n]], {n, 15}] CROSSREFS Cf. A000081, A000669, A001678, A141268, A316471, A316471, A316475, A316495. Sequence in context: A049937 A026754 A291247 * A032170 A084081 A106376 Adjacent sequences:  A316694 A316695 A316696 * A316698 A316699 A316700 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 10 2018 EXTENSIONS a(18)-a(22) from Robert Price, Sep 14 2018 STATUS approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)