Coefficients of vector addition of class II representations of $SU(n)$

The tree method is used to obtain a formula for the coefficients of vector addition of class II representations of $SU(n)$. It is shown that the coefficients of vector addition of $SU(n)$ are determined by the Clebsch–Gordan coefficients of $SU(2)$ and the hypergeometric functions $_3F_2$ of unit argument.