OFFSET
1,5
COMMENTS
We say that a tree is square if it has the same height as number of leaves.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
EXAMPLE
The a(1) = 1 through a(6) = 5 ordered trees:
o . (oo) . ((o)oo) ((o)(o)o)
((oo)o) ((o)(oo))
((ooo)) ((o)o(o))
(o(o)o) ((oo)(o))
(o(oo)) (o(o)(o))
(oo(o))
MATHEMATICA
aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[aot[n], Count[#, {}, {0, Infinity}]==Depth[#]-1&]], {n, 1, 10}]
PROG
(PARI) \\ R(n, f) enumerates trees by height(h), nodes(x) and leaves(y).
R(n, f) = {my(A=O(x*x^n), Z=0); for(h=1, n, my(p = A); A = x*(y - 1 + 1/(1 - A + O(x^n))); Z += f(h, A-p)); Z}
seq(n) = {Vec(R(n, (h, p)->polcoef(p, h, y)), -n)} \\ Andrew Howroyd, Jan 01 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2022
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Jan 01 2023
STATUS
approved