OFFSET
1,7
COMMENTS
An unlabeled rooted tree is leaf-balanced if all branches from the same root have the same number of leaves. It is series-reduced if all positive out-degrees are greater than one.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..84
EXAMPLE
The a(13) = 5 trees: (((oo)(oo))(oooo)), ((ooooo)(ooooo)), ((ooo)(ooo)(ooo)), ((oo)(oo)(oo)(oo)), (oooooooooooo).
MATHEMATICA
alltim[n_]:=alltim[n]=If[n===1, {{}}, Join@@Function[c, Select[Union[Sort/@Tuples[alltim/@c]], And[SameQ@@(Count[#, {}, {0, Infinity}]&/@#), FreeQ[#, {_}]]&]]/@IntegerPartitions[n-1]];
Table[Length[alltim[n]], {n, 20}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 06 2018
EXTENSIONS
a(51) onward from Robert G. Wilson v, Jan 07 2018
STATUS
approved