5-12 Let the polynomial $1-x+x^{2}-x^{3}+\cdots+x^{16}-x^{17}$ be written as $a_{0}+a_{1} y+a_{2} y^{2}+a_{3} y^{3}+\cdots+a_{16} y^{16}+a_{17} y^{17}$, where $y=x+1$, and each $a_{i}$ is a constant, find $a_{2}$.