OFFSET
1,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
EXAMPLE
The a(2) = 1 through a(6) = 15 trees:
(o) ((o)) ((oo)) (((oo))) (((ooo)))
(o(o)) ((o)(o)) ((o)(oo))
(((o))) ((o(o))) ((o(oo)))
(o((o))) ((oo(o)))
((((o)))) (o((oo)))
(o(o)(o))
(o(o(o)))
(oo((o)))
((((oo))))
(((o)(o)))
(((o(o))))
((o)((o)))
((o((o))))
(o(((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}]&]], {n, 0, 10}]
PROG
(PARI)
R(n) = {my(A = O(x)); for(j=1, n, A = x*(y - 1 + exp( sum(i=1, j, 1/i * subst( subst( A + O(x*x^(j\i)), x, x^i), y, y^i) ) ))); Vec(A)};
seq(n) = {my(A=R(n)); vector(n, n, vecsum(Vecrev(A[n]/y)[1..n\2]))} \\ Andrew Howroyd, Dec 30 2022
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 23 2022
EXTENSIONS
Terms a(19) and beyond from Andrew Howroyd, Dec 30 2022
STATUS
approved