OFFSET
1,6
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
Conjectures from Chai Wah Wu, Apr 14 2024: (Start)
a(n) = 9*a(n-1) - 32*a(n-2) + 58*a(n-3) - 58*a(n-4) + 32*a(n-5) - 9*a(n-6) + a(n-7) for n > 7.
G.f.: x^5*(-x^2 + x - 1)/((x - 1)^3*(x^2 - 3*x + 1)^2). (End)
EXAMPLE
The a(5) = 1 and a(6) = 8 ordered trees:
((o)(o)) ((o)(o)o)
((o)(oo))
((o)o(o))
((oo)(o))
(o(o)(o))
(((o))(o))
(((o)(o)))
((o)((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) \\ Needs R(n, f) defined in A358590.
seq(n) = {Vec(R(n, (h, p)->polcoef(subst(p, x, x/y), -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