  In this paper, we consider the sums of non-negative integer valued
$m$-dependent random variables, and its approximation to the power series
distribution. We first discuss some relevant results for power series
distribution such as Stein operator, uniform and non-uniform bounds on the
solution of Stein equation, and etc. Using Stein's method, we obtain the error
bounds for the approximation problem considered. As special cases, we discuss
two applications, namely, $2$-runs and $(k_1,k_2)$-runs and compare the bound
with the existing bounds.
