I've been trying to find an algorithm to list all binary trees of a given height $h$. Note that I'm not trying to count them: the number of such trees is given in the OEIS (A001699). All the algorithms that I have been able to see list all binary trees for a given number of nodes. A very inefficient way of solving the problem would proceed by checking all the trees with a number of nodes between $h+1$ and $2^{h+1}-1$, but this is not great at all. Any pointers or references would be much appreciated.
Algorithm for listing all binary trees of a given height
algorithms;binary trees;enumeration