AVL tree is balanced binary search tree.
so maximum no of nodes at height 'h' is $2^{h+1}-1$
Left subtree contains quarter of max no of nodes at height 'h' =$\frac{2^{h+1}-1}{4}$.
Right subtree contains on fifth of max nof nodes at height 'h' is=$\frac{2^{h+1}-1}{5}$.
Finally total no of nodes in AVL tree is=sum of nodes at left subtree+sum of nodes at right subtree+1.
=$\frac{2^{h+1}-1}{4}$.+$\frac{2^{h+1}-1}{5}$.+1
=.$\frac{9*2^{h+1}+11}{20}$