The coefficient of x<sup>n</sup> in the expansion of (1 - 2x + 3x<sup>2</sup> - 4x<sup>3</sup> + ... to ∞)<sup>-n</sup> is
\(1 - 2x + 3x^2 - 4x^3 + \dots = (1 + x)^{-2}\)
So \((1 - 2x + 3x^2 - \dots)^{-n} = (1 + x)^{2n}\).
The coefficient of \(x^n\) is \(\binom{2n}{n} = \frac{(2n)!}{(n!)^2}\).
Answer: (C)
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