OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..100
EXAMPLE
The a(3) = 2 and a(4) = 17 trees:
((o)(oo)) (((o))(ooo))
(o(o)(o)) (((o)(ooo)))
(((oo))(oo))
(((oo)(oo)))
((o)((ooo)))
((o)(o(oo)))
((o)(oo(o)))
((o(o)(oo)))
((oo)(o(o)))
((oo(o)(o)))
(o((o))(oo))
(o((o)(oo)))
(o(o)((oo)))
(o(o)(o(o)))
(o(o(o)(o)))
(oo((o)(o)))
(oo(o)((o)))
MATHEMATICA
art[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[art/@c], OrderedQ], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[art[n], Count[#, _[__], {0, Infinity}]==Count[#, {}, {0, Infinity}]==Depth[#]-1&]], {n, 2, 15, 2}]
PROG
(PARI) \\ Needs R(n, f) defined in A358589.
seq(n) = {Vecrev(R(2*n, (h, p)->if(h<=n, x^h*polcoef(polcoef(p, 2*h, x), h, y))), -n)} \\ Andrew Howroyd, Jan 01 2023
CROSSREFS
These trees are ranked by A358592.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 23 2022
EXTENSIONS
Terms a(10) and beyond from Andrew Howroyd, Jan 01 2023
STATUS
approved