Prove the equality $\frac1{(1-x)^4} = \sum\limits_{n=0}^∞ ((n+1)(n+2)(n+3))x^n$

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$$\frac1{(1-x)^4} = \sum\limits_{n=0}^∞ ((n+1)(n+2)(n+3))\frac{x^n}6$$ So. I have been stuck with this series for quite a while and don't know how to prove this equality.