All About Factorials!

\[ f(x) = \large \sum_{m=1}^{x} m! \]

Let \(f\) be the function of the sum of all factorials under \(x\) as shown above. If \(n\) is a positive integer such that it satisfies the constraint \(n = f(2a) - f(a) = (a!)^{2}(b!)\) for some positive integers \(a\) and \(b\) greater than 1, what is the value of \(n\)?

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