Let $\{f_n(x)\}$ be a sequence of polynomials defined as $f_1(x) = (x - 2)^2$, $f_{n+1}(x) = (f_n(x) - 2)^2$; $n \ge 1$.
What are the coefficients of the polynomial inductively defined as $f_1=(x-2)^2\,\,\,;\,\,\,f_{n+1}=(f_n-2)^2$?