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

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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