Coefficient in a polynomial

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The coefficient of $x_1^{r_1}...x_k^{r_k}$ in $(x_1 +x_2+...x_k)^n$ is ${n \choose r_1r_2\dots r_k}$.

How would I go about finding the coefficient of $x_1^{r_1}...x_k^{r_k}$ in $(x_1^2+\dots+x^2_k)^n$.

Thanks!