多项式递推trick

数论trick \[F_n(x)=\prod_{i=0}^n(1-p^ix) \]可以考虑 \[F_n(px)=\prod_{i=0}^{n}(1-p^{i+1}x)=\prod_{i=1}^{n+1}(1-p^ix)=F_n(x)\frac{1-p^{n+1}x}{1-x} \]即 \[(1-x)