HMMT 2014 U28

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Answer

Let $f(n)$ and $g(n)$ be polynomials of degree 2014 such that $f(n)+(-1)^{n} g(n)=2^{n}$ for $n=$ $1,2, \ldots, 4030$ . Find the coefficient of $x^{2014}$ in $g(x)$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3^{2014}}{2^{2014} \cdot 2014!}

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