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I am trying to find an exact formula for the following:

$\sum\limits_{i=0}^{n}{\binom{2n}{n-i}\frac{2i^2+i}{n+i+1}}$

I don't think this should be too bad with a rearrangement of terms, but I keep getting stuck.

  • 0
    [WA doesn't seem to give a nice formula...](http://www.wolframalpha.com/input/?i=summation+C%282n%2Cn-k%29*%282k%5E2%2Bk%29%2F%28n%2Bk%2B1%29+from+k+%3D+0+to+n)2012-11-29
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    But that is without the other part of the sum and infinite.....2012-11-29
  • 0
    Ah, never mind, the link wasn't working properly at first. I have been told there is a nice exact form though2012-11-29

2 Answers 2