AVL-trees

AVL-tree — a balanced binary search tree by height: for each vertex, the heights of its two subtrees differ by no more than $1$. AVL-trees are named after the inventors G. M. Adelson-Velsky and E. M. Landis, using the first letters of their surnames.

For a given number of vertices, there may be several different AVL-trees. For example, there are six AVL-trees with five vertices.

Also, trees with the same number of vertices can have different heights. For example, there are trees with seven vertices of heights $2$ and $3$.

Given $n$ and $h$, find the number of AVL-trees with $n$ vertices and height $h$. Since the answer can be very large, output the remainder of dividing this number by $786433$.