How could we show that: $\prod_{0 \le j \ne i \le n} \frac{n+1-j}{i-j} = \frac{(n+1)!}{(n+1-i)\cdot i! \cdot (n-i)!}(-1)^{(n-i)} .$
The module suggest we could reduce it by simply writing \prod_{0 \le j \ne i \le n} \frac{n+1-j}{i-j} = \frac{(n + 1)n \cdots (n + 1 − (i − 1))(n + 1 − (i + 1)) \cdots 1}{i(i − 1) \cdots 1 · (−1) \cdots (−(n − i))} , but I am not able to figure out the result from here.
Please explain your answer.