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Is there a nice expression for the coefficients of $\prod_{i=0}^{n} (x-a^i)$, which are (up to sign) the elementary symmetric polynomials evaluated on a geometric progression?

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What you wrote is related to q-Pochhammer symbol, $\prod_{i=0}^n \left(x- a^i\right) = x^{n+1} \left(\frac{1}{x}; q \right)_{n+1}$ – Sasha Jun 21 '12 at 18:51

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