Not as simple as it seems.

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 \(P_{20}(x)\) ?

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