\begin{aligned}
 \prod_{i\in\omega+2}(i+\omega\cdot 2+i)
 & = \Big(\prod_{i\in\omega}(i+\omega\cdot 2+i)\Big)\cdot(\omega+\omega\cdot 2+\omega)\cdot(\omega+1+\omega\cdot 2+\omega+1) \\
 & = \Big(\sup_{n\in\omega}\prod_{i\in n}(\omega\cdot 2+i)\Big)\cdot (\omega\cdot 4)\cdot(\omega\cdot 4+1) \\
\end{aligned}