Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Thanks a lot. I still have some difficulties understanding why $(-1)^{j-1}\frac{(k-j-1)!}{(i-1)!}{i+j-k-1\choose j-1} \geq 0$, though, as $(-1)^{j-1}$ is negative for even $j$.
