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Non-recursive expression for coefficients of the derivative of the logarithm of a power series
Let $f :(-1,1) \to \mathbb{R};\ \ f(x)=\sum_{n=0}^\infty a_n x^n$ be an analytical function expressible as a power series.
Also, let
$$g : (-1,1) \to \mathbb{R}; \ \ g(x)=\frac{d}{dx} \log{f(x)} = …