Let $a_1,\cdots,a_n$ be n positive consecutive integers. So I want to know if there exists a close combinatorial form for the coefficient of $x^k$ in $$(x+a_1)(x+a_2)\ldots (x+a_n) .$$ In particular is there something nice for $a_1=1,\ldots,a_n=n$?
2026-03-25 20:09:32.1774469372
Combinatorial identity
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