I'm having some trouble finding a closed formula for this quantity:

\begin{align\*}
\sum\_{j} \binom{n}{j}\binom{j}{n-j}
\end{align\*}
I know that this size is equal to
\begin{align\*}
\sum\_{j} \binom{n}{j}\binom{n-j}{j}
\end{align\*}
And also
\begin{align\*}
\sum\_j \binom{n}{2j}\binom{2j}{j}
\end{align\*}
All these sums are over all allowed $j$, that is, so the lower index in the binomial coefficient is not greater than the upper, and is not negative. Can someone help me? Thanks :)

Edit: It seems like people agree that there might not be a simple closed form for this sum.

Edit: Apparently, this sum is the n-th term in the sequence of central trinomial coefficients, which do not have a closed form that are on my level. I did not know that at the time. Thanks for your answers!