P350: Enumeration of all binary trees with $n$ vertices

P350: Enumeration of all binary trees with $n$ vertices
Input:
An integer $n$.
Output:
All binary trees with $n$ vertices.
Complexity:
$O(1)$ time per solution.
Comment:
A loopless generation algorithm is an algorithm where the amount of computation to go from one object to the next is $O(1)$.
Reference:
[VanBaronaigien1991] (Bibtex)