How to prove a formula using Vandermode's Convolution Formula

Asked Sep 30 '14 at 02:37

Active Sep 30 '14 at 03:32

Viewed 67 times

Need to prove this formula enter image description here

based on Vandermode's Convolution Formula which is enter image description here

not sure how to prove first one based on second one.

It could make sense if C(n, i) = C(n, r-i)
though, I am not sure if such identity exists. If it exists than second formula is pretty much first formula with just n and m being same value. If there is such an identity - please tell me how its name :) I will be thankful for your explanation.

edited Sep 30 '14 at 03:32

asked Sep 30 '14 at 02:37

YohanRoth

1,627

5

What happens in the second equation when $n = m = r$? – Jonny Sep 30 '14 at 02:41
Also, $\displaystyle{n\choose k}={n\choose n-k}$ – Lucian Sep 30 '14 at 02:47
1

+1 for the username. But it's Vandermonde. – darij grinberg Sep 30 '14 at 03:22
possible duplicate of Combinatorial proof of summation of $\sum_{k = 0}^n {n \choose k}^2= {2n \choose n}$ – andre Sep 30 '14 at 22:08

How to prove a formula using Vandermode's Convolution Formula

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