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October 11th, 2017, 09:15 PM   #1
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Exclamation Simplify the sum

How would you simplify the following sum?

The parentheses refer to combinations (n choose r). The outcome should be a function of y. However, I cannot figure out how to simplify this. Any recommendations?
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October 11th, 2017, 10:20 PM   #2
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Mathematica chugged away at it for a while and didn't come up with anything.
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October 12th, 2017, 04:36 PM   #3
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I figured it out.
It's Vandermonde's identity.

https://en.wikipedia.org/wiki/Vandermonde%27s_identity
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