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)