1986 AIME Problem 11

The polynomial 1-x+x^{2}-x^{3}+\cdots+x^{16}-x^{17} may be written in the form a_{0}+a_{1} y+a_{2} y^{2}+a_{3} y^{3}+\cdots+a_{16} y^{16}+a_{17} y^{17}, where y=x+1 and the a_{i} 's are constants. Find the value of a_{2}.