Web Reference: In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series. Also if we consider a class A of objects to be enumerated, we call generating function of this class the generating function A(x) = anxn; When we write down a nice compact function which has an infinite power series that we view as a generating series, then we call that function a generating function.
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