How to put a formula into a table cell

You cannot use \begin{equation}...\end{equation} inside a table cell. If you want it to look like a displayed equation, you can do this:

3 & \(\displaystyle \sum_{n=1}\nolimits' C_n \) & $2$ & $2(n+1)$ \\

Here, \( ... \) is inline math (more-or-less equivalent to $ ... $), and \displaystyle is self-explanatory: it typesets the equation in the style as it was a displayed math.

You can actually put \begin{equation}...\end{equation} in a tabular cell, but you need to box it up first, either using a vbox, minipage, parbox, or something similar.

Whether or not that's a good idea is another issue; if your tabular is floating then it's almost certainly a bad idea (as the numbering might get messed up)

3 & \vbox{\begin{equation} \sum_{n=1}\nolimits' C_n \end{equation}} & $2$ & $2(n+1)$ \\
4 & \parbox{3cm}{\begin{equation} \sum_{n=1}\nolimits' C_n \end{equation}} & $2$ & $2(n+1)$ \\
5 & \begin{minipage}{4cm}\begin{equation} \sum_{n=1}\nolimits' C_n \end{equation}\end{minipage} & $2$ & $2(n+1)$ \