Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Could someone help me manipulate this sum? I need to be able to extract the coefficient of $x^{n-1}$ in the following: $\sum_{i=0}^{\infty}\sum_{j=0}^{\infty}\binom{n-1}{i}\binom{n+j-1}{j}x^{i+2j}$. Ideally, this would also be something that has a closed form, since extracting this coefficient as a sum wouldn't help the other calculations that I need to do. This manipulation is actually part of a larger problem, but this is the part that I am currently stuck on. Help is appreciated :).

Thanks!

share|improve this question
    
Does anyone know an identity for this? Or could someone show me how to manipulate this sum> –  Nizbel99 Nov 9 '12 at 1:56

1 Answer 1

By inspection, $$\sum_{j=0}^{\lfloor (n-1)/2\rfloor} \binom{n+j-1}{j}\binom{n-1}{n-1-2j}.$$ I'm not aware of any closed form for such a sum.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.