An ordinary generating function is a formal power series that encodes a sequence of numbers as coefficients of the powers of a variable. It is expressed in the form $$A(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \ldots$$ where each coefficient $$a_n$$ represents the nth term of a sequence. This tool is powerful for solving problems in combinatorics, helping to find closed forms for sequences, analyze recurrence relations, and model various counting problems.
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