Show that $\frac{(J-1)!}{2!(J-3)!}= \sum_{h=2}^{J-1}(h-1) $

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Could you help me to show that $$ \frac{(J-1)!}{2!(J-3)!}= \sum_{h=2}^{J-1}(h-1) $$ where "$!$" denotes the factorial function?

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$$\sum_{h=2}^{J-1} (h-1) = \sum_{h=1}^{J-2} h = \frac{(J-2)(J-1)}{2}= \frac{(J-1)!}{2!(J-3)!}$$