I have the following sum \begin{equation} \sum_{r_1=q+1}^{\tau}\dots\sum_{r_\lambda=q+1}^{\tau}{\tau\choose r_1,\dots,r_\lambda,\taur_1\dots r_\lambda} (\Lambda\lambda)^{\taur_1\dotsr_\lambda} \end{equation} and would like to estimate its value. Any ideas or techniques to do this? By the way, it is not always the case that $\tau>>q$, so the entire range of possibilities is necessary.
