OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
a(n + 1) = Sum_{d|n} binomial(A000081(n/d) + d - 1, d).
EXAMPLE
The a(5) = 6 trees: ((((o)))), (((oo))), ((o(o))), ((ooo)), ((o)(o)), (oooo).
MATHEMATICA
r[n_]:=r[n]=If[n===1, 1, Sum[Product[Binomial[r[x]+Count[ptn, x]-1, Count[ptn, x]], {x, Union[ptn]}], {ptn, IntegerPartitions[n-1]}]];
Table[If[n===1, 1, Sum[Binomial[r[(n-1)/d]+d-1, d], {d, Divisors[n-1]}]], {n, 40}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 20 2018
STATUS
approved