Knuth's hook length formula for trees

Statement

Let $T$ be a plane binary tree, and let $f_{T}$ be the number of increasing labelings of vertices of $T$ .

We define the hook length of a vertex $v \in T$ as the number of descendants of $v$ including $v$ . (ie. the size of the subtree rooted at $v$ ).

Then,

f_{T} = \frac{n!}{\prod_{v \in T} h (v)}