Notation: why $f_\lambda$ in the hook-length formula?

I just learned the hook-length formula: the number of Standard Young Tableaux of size $n$ and shape $\lambda$ is$$\frac{n!}{\prod_\limits{x} \operatorname{hook}(x)}$$where the product runs over all boxes of the diagram.

This quantity is usually called $f_\lambda$. Why is it like this?I see no relation between SYT and the letter $f$. Maybe it has to do with the degree of representations, but that would not indicate an $f$ as the standard notation.