The polynomial

\(1-x+x^{2}-x^{3}+…+x^{16}-x^{17}\)

may be written in the form

\(a_{0}+a_{1}y+a_{2}y^{2}+…+a_{16}y^{16}+a_{17}y^{17}\)

where \(y=x+1\) and \(a_{i}\)'s are constants. Find \(a_{2}\).

(第四届AIME1986 第11题)