IMO 1978 LL BUL2

If

IMO 1978 LL BUL2

Origin: BUL

Problem

If f(x) = (x + 2x2 + \cdot \cdot \cdot + nxn)2 = a2x2 + a3x3 + \cdot \cdot \cdot + a2nx2n, prove that an+1 + an+2 + \cdot \cdot \cdot + a2n = n + 1 5n2 + 5n + 2 .