Find the coefficient

Algebra Level 5

$\large 1-x+x^2-x^3+\ldots+x^{16}-x^{17}$ 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 $a_2$ .