Let $n,k$ be positive integers. The expansion of $(x_1+\dots+x_k)^n$ is given by
$$(x_1+\dots+x_k)^n=\sum\frac{n!}{n_1!n_2!\dots n_k!}x_1^{n_1}x_2^{n_2}\dots x_k^{n_k},$$
where the sum is taken over all sequences $n_1,n_2,\dots,n_k$ of non-negative integers such that $n_1,n_2+\dots+n_k=n$. What is the coefficient of $x^5$ in the expansion of $(1+3x+2x^2)^4$?