Finding the coefficient in the expansion of $\prod\limits_{m=1}^N \left(1-R^mA\right)$

I understand that $$\prod\limits_{m=1}^N \left(1-R^mA\right)$$ is a polynomial in $A$, and so can be written as $\sum\limits_{k=0}^N c_k A^k$ for some coefficients $c_k$.

I can't seem to figure out a closed form expression of $c_k$, any ideas?

• See the $q$-Pochhammer symbol. – orlp Oct 2 '17 at 15:30
• What do you actually need? A closed-form formula, just a formula or an algorithm? – Lwins Oct 2 '17 at 15:44

• would $c_k$ then be be $(-1)^k$ multiplied with everything else apart from $a^k$? thanks – Tiana Oct 2 '17 at 16:12