Evaluate $\sum_{i=r}^n{i \choose r}^2$ where $n,r\in \mathbb{N},n>r$. This looks like the hockey stick identity but I can't find a way to evaluate it without a computer. Can someone help me out?
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I am about 75% certain that this expression has no nice closed form, but I'm gonna think about it for a while more before saying anything too definitive – Oct 08 '15 at 14:30
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I found it...https://oeis.org/A086020 It seems there is a closed form but I cant see any intuitive way how it was determined. What do you think? – 1-___- Oct 08 '15 at 15:03
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@user2770287 A086020 would be only a particular case ($r=3$), no? – leonbloy Jan 18 '16 at 14:42
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Yes, I started by looking at a particular case rather than in general. – 1-___- Jan 25 '16 at 16:24