Shew that the coefficient of \( x^{n} \) in the expansion of \( \frac{x}{(1-x)^{2}-c x} \) is \(...

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Shew that the coefficient of \( x^{n} \) in the expansion of \( \frac{x}{(1-x)^{2}-c x} \) is \( n\left\{1+\frac{n^{2}-1}{3 !} c+\frac{\left(n^{2}-1\right)\left(n^{2}-4\right)}{5 !} c^{2}+\frac{\left(n^{2}-1\right)\left(n^{2}-4\right)\left(n^{2}-9\right)}{7 !} c^{3}+\ldots\right\} \)
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