Oh! its a series, or is it ?

Level pending

If the summation \(S=\displaystyle \sum_{n=1}^{\infty} \dfrac{n^2+1}{n+2} \cdot \dfrac{x^n}{n!}\) can be written as a function \(f(x)\), find \(\lceil f(1) \rceil \), where \(\lceil x \rceil \) is the cieling function.

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