Let $C = 1 + |s_1| + \cdots + |s_r|$. Show that $D^n v_n(k) \in \mathbf{Z}$ and that there exists a real number $c_2 > 0$ such that $$|v_n(k)| \leq c_2 A^n C^k \text{ for all } n \geq kr.$$
Let $C = 1 + |s_1| + \cdots + |s_r|$. Show that $D^n v_n(k) \in \mathbf{Z}$ and that there exists a real number $c_2 > 0$ such that
$$|v_n(k)| \leq c_2 A^n C^k \text{ for all } n \geq kr.$$