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Let $s(m,n)$ denote the Stirling numbers of the first kind. For $m,n\in\mathbb{N}$, define \begin{equation} \mathcal{Q}(m,n)=(-1)^n\sum_{\ell=0}^{2n} \binom{m+\ell-1}{m-1} s(m+2n-1,m+\ell-1)\biggl(\...

This is a well-known problem and is about counting the number of distinct numbers in the $n \times n$ multiplication table. The very problem has been discussed in-depth and, as such, I require no ...