\begin{aligned}
 \prod_{j\in i}(\omega+(i+1)^j)
 & = (\omega+1)\cdot(\omega+(i+1))\cdot(\omega+(i+1)^2)\cdot\cdots\cdot(\omega+(i+1)^{i-1}) \\
 & = \omega^i+\text{ne\v{s}to}
\end{aligned}