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%I #8 Sep 14 2018 14:33:10
%S 1,1,2,5,10,24,49,112,241,548,1218,2839,6547,15572,37179,90555,222065,
%T 552576,1384820,3506475,8936121,22941280
%N Number of series-reduced locally disjoint rooted trees with n unlabeled leaves.
%C 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.
%e The a(5) = 10 trees:
%e o(o(o(oo))))
%e (o(o(ooo)))
%e (o((oo)(oo)))
%e (o(oo(oo)))
%e (o(oooo))
%e (oo(o(oo)))
%e (oo(ooo))
%e (o(oo)(oo))
%e (ooo(oo))
%e (ooooo)
%e Missing from this list but counted by A000669 are ((oo)(o(oo))) and ((oo)(ooo)).
%t disjointQ[u_]:=Apply[And,Outer[#1==#2||Intersection[#1,#2]=={}&,u,u,1],{0,1}];
%t nms[n_]:=nms[n]=If[n==1,{{1}},Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]],disjointQ],{ptn,Rest[IntegerPartitions[n]]}]];
%t Table[Length[nms[n]],{n,15}]
%Y Cf. A000081, A000669, A001678, A141268, A316471, A316471, A316475, A316495.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Jul 10 2018
%E a(18)-a(22) from _Robert Price_, Sep 14 2018
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