Question: Shortening an expression

I have the following expression


The parameters i and N are nonnegative integers and i is less than or equal to N. The purpose is to make it as short as possible. Based on my experience, it could be expressed as a small binomial expression or as a sum of two or three binomials. However, by Maple commands the conversion does not give me binomials or any smaller expression.

Is there any way for the conversion to binomials or any other conversion to shorten the expression?

I appreciate any help.

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