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Power Serieshard
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Consider the product of two series f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞​xn and g(x)=∑n=0∞xnn!g(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}g(x)=∑n=0∞​n!xn​. What is the coefficient of x2x^2x2 in their Cauchy product (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x)?