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How to find the coefficient of $x^k$ in the expression $\prod_{p=2}^n (1+xp) $

From representation $$\prod_{p=2}^n (1+xp) = (-x)^{n+1} (-1/x)_{n+1} (1+x)^{-1}= \sum_{i\geq 0} s_1(n+1,i) (-x)^{n+1-i}\cdot \sum_{j\geq0} (-x)^j, $$ it follows that the coefficient of $x^{k-1}$ in ...
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