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_1y+a_2y^2+\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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.