### writting a code for finding the kostant partition function

How to write a code for finding the kostant partition function for the elements of root lattice of $A_{1}^{(1)}$ which is defined as follows:
$K(\beta)$ = the co-efficient of $e^{\beta}$ in $\prod _{\alpha \in \bigtriangleup}(1-e^{\alpha})$ where $\bigtriangleup$ is the set of positive roots of $A_{1}^{(1)}$ and $\beta$ is an element of the root lattice ?