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Let $a = \min (x^2+2x+3)$ and $b = \displaystyle \lim_{x \to 0} \frac { \sin x \ \cos x}{e^x - e^{-x} }$ for real parameter $x$.

What is the value of $\displaystyle \sum_{r=0}^n a^r b^{n-r}$?

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