A closed formula for linear recurrences with constant coefficients

Given a linear recurrence of the form $c_n=a_1{c}_{n-1}+\cdots +a_j{c}_{n-j}$, it is well-known that $c_n={\sum }_r{p}_r(n)r^n$, where the sum is taken over the set of characteristic roots and each $p_r(n)$ is some polynomial. We give a closed formula for the coefficients of each polynomial $p_r(n)$ for any linear recurrence of this form.