\[\large 1-x+x^2-x^3+\ldots+x^{16}-x^{17}\] The polynomial above may be written in the form \[a_0 + a_1y + a_2y^2+...+a_{16}y^{16}+a_{17}y^{17}\] where \(y=x+1\) and \(a_i's\) are constants. Find \(a_2\).

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