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
Andrew Howroyd, Table of n, a(n) for n = 1..500
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}]
PROG
(PARI) seq(n)={my(v=vector(n)); v[1]=x/(1-x) + O(x*x^n); for(k=2, n, v[k]=x*sumdiv(k, d, if(d<k, v[d]^(k/d)))/(1-x) ); Vec(vecsum(v) + O(x*x^n))} \\ Andrew Howroyd, Dec 13 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 16 2018
EXTENSIONS
Terms a(17) and beyond from Andrew Howroyd, Dec 13 2020
STATUS
approved