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Random tensor models are generalizations of matrix models which also supporta 1/N expansion. The dominant observables are in correspondence with sometrees, namely rooted trees with vertices of degree at most $D$ and linescolored by a number $i$ from 1 to $D$ such that no two lines connecting avertex to its descendants have the same color. In this Letter we study byindependent methods a generating function for these observables. We prove thatthe number of such trees with exactly $p_i$ lines of color $i$ is$\frac{1}{\sum_{i=1}^D p_i +1} \binom{\sum_{i=1}^D p_i+1}{p_1} ...\binom{\sum_{i=1}^D p_i+1}{p_D}$.

Counting Line-Colored D-ary Trees