visiting $n$ distinct sites in a random walk of $n$ steps on $\mathbb{Z}^2$

Question

Consider the symmetric random walk on $\mathbb{Z}^2$. I am looking for references about the number of ways to visit $n$ distinct sites in $n$ steps where I don't count the origin, so visiting $n+1$ distinct sites in $n$ steps is not possible. Thank you very much.