Double Sum and Double Product

\[\displaystyle \sum^{n}_{p=1} \sum^{n}_{m=p} \dbinom{n}{m} \dbinom{m}{p}\]

If the value of the above expression is in the form \(a^n-b^n\), where \(a\) and \(b\) are prime numbers, find \(a+b\).

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