Major downfall

Calculus Level pending

\[ \large \sum_{n=0}^\infty \frac1{n!} \left(n + (n-1)x^2\right)^2 \frac{x^{2n}}{(1+x^2)^{n+2}} \exp\left(-\frac{x^2}{1+x^2}\right) \]

If \(f(x) \) denote the function above, find the value of \(f(2) \).

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