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)