Let $$P_0(x) = x^3 + 313x^2 - 77x - 8\,$$ . For integers $$n \ge 1\,$$ , define $$P_n(x) = P_{n - 1}(x - n)\,$$ . What is the coefficient of $$x\,$$ in $$P_{20}(x)\,$$ ?

(第十一届AIME1993 第5题)