I am trying to find a closed form for the following double summation.
$\sum_{n=0}^{N} \sum_{m=0}^{N-n} \binom{n}{m}\binom{N-n}{m} x^n y^m$
It seems to be like Vandermonde's identity. Can anyone provide any suggestion?
2026-04-01 18:42:31.1775068951
Finding closed form for double summation binomial
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