MathDB

Let

n

and

k

be integers such that

0\leq k\leq n

. Prove that

\sum_{u=0}^{k}\binom{n+u-1}{u}\binom{n}{k-2u}=\binom{n+k-1}{k}

. Note that we use the following conventions:

\binom{r}{0}=1

for every integer

r

;

\binom{u}{v}=0

u

is a nonnegative integer and

v

is an integer satisfying

v<0

v>u

. Darij

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