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The polynomial $1 - x + x^2 - x^3 + \ldots +x^{16} - x^{17}$ may be written in the form:

$a_0 + a_1y + a_2y^2 + \ldots +a_{16}y^{16} + a_{17}y^{17},$

where $y=x+1$ and $a_i$ are constants. Find $a_2$.

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