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I am wondering if it is possible to calculate or approximate the following sum $$ \sum_{k=0}^l\frac{(l-2k)^p(2l+k(k-1))l^{k-1}}{(k+3)(k+2)} $$here $p \geq 2$.

Thank you.

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You could just add them up :) Are you asking for a closed form expression with $p$ variable? Also, it would be nice if you provided some context for where you encountered this and what methods you have tried or are available to you. –  Eric Gregor Apr 29 '12 at 0:05
    
Yes, I am asking for the closed form expression. I got this sum from $\sum_{k=0}^n(n-2k)^p\frac{{ n \choose k}{2m-n \choose m-k}}{{2m \choose m}}$. it was my question not long time ago. I still trying to find an answer for it. –  Michael Apr 29 '12 at 0:51
    
Can you find a closed form for $p=0,1,2,3$? Can you give a link to your previous question? –  Phira Apr 30 '12 at 20:52
    
For odd $p$ the sum is $0$. math.stackexchange.com/q/131826 –  Michael May 1 '12 at 17:25

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