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Long ago , I once saw a nontrivial appealing binomial type of identity that I never saw again. It was something along the line of $\Sigma$$\binom{a(x)}{b(y)}$= where $a$ and $b$ where polynomials not all constant or linear.

I was never able to find that identity again and only realised the imho weird fact of polynomials involved much later. The sum had a simple parameter such as from 0 to $n$ or such and the polynomials were of degree at most 5. Also the amount of variables was low. Im sorry if this is a bit vague but I can't recall much more. Does anybody have an idea what this identity might have been ? Or where it comes from ? Or how to prove it ? I believe it was related to number theory and divisibility but im not completely sure. Maybe it relates to Apery's proof of the irrationality of zeta(3) but again im not sure. I did not see a proof of it , but at the time i did test it numerically and it hold. I guess that makes this a reference request unless someone know alot about these rare identities or I missed something trivial.

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