All Questions

Consider $n$ numbers randomly generated by independent generators that can produce integers from $0$ to $n$. How many of these integers will be missing on average for large $n$? If $p_{k,n}$ is the ...

Having some work done, here is a refined version of my initial question. For integer $m>0$ and $0\le q\le m$, consider the sum $$ S(m,q) = \sum_{i=0}^{m-q} \binom{m}{i} \binom{m-i}{q}^2. $$ I ...