## Taylor expansion of $\prod_{i=1}^n(1-x_i)^{-1/2}$ around 0

What is the Taylor expansion of $$\prod_{i=1}^n\frac{1}{\sqrt{1-x_i}}$$ around $$(0,0,…,0)$$？I know that we can write it as $$\prod_{i=1}^n\left(1+\sum_{k=1}^{\infty}\frac{(2k-1)!!x_i^k}{(2k)!!}\right)$$ But how to simplify it?