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 A304175 Number of leaf-balanced rooted plane trees with n nodes. 5
 1, 1, 2, 5, 12, 27, 59, 128, 277, 597, 1280, 2730, 5794, 12248, 25836, 54508 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A rooted plane tree is leaf-balanced if every branch of the root has the same number of leaves, and every branch of the root is itself leaf-balanced. LINKS EXAMPLE The a(5) = 12 leaf-balanced plane trees:   ((((o)))), (((oo))), (((o)o)), ((o(o))), ((ooo)),   (((o))o), (o((o))), ((o)(o)),   ((o)oo), (o(o)o), (oo(o)),   (oooo). Missing from this list are ((oo)o) and (o(oo)). MATHEMATICA lbplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[lbplane/@c], SameQ@@(Count[#, {}, {0, Infinity}]&/@#)&], {c, Join@@Permutations/@IntegerPartitions[n-1]}]]; Table[Length[lbplane[n]], {n, 10}] CROSSREFS Cf. A000081, A000108, A001003, A001006, A003238, A007853, A126120, A291442, A291443, A304173. Sequence in context: A083378 A116712 A000102 * A086589 A299270 A190171 Adjacent sequences:  A304172 A304173 A304174 * A304176 A304177 A304178 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 16 2018 STATUS approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)