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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