AIME 1986 problem

Algebra Level 4

The polynomial 1x+x2x3++x16x171 - x + x^2 - x^3 + \ldots +x^{16} - x^{17} may be written in the form:

a0+a1y+a2y2++a16y16+a17y17,a_0 + a_1y + a_2y^2 + \ldots +a_{16}y^{16} + a_{17}y^{17},

where y=x+1y=x+1 and aia_i are constants. Find a2a_2.

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