Just H and S

Calculus Level 3

If \[H = \displaystyle \sum_{n=1}^{\infty} \frac{n^{3}}{(n - 1)!}\] and \[S = \displaystyle \sum_{n=1}^{8} \frac{n}{1+n^{2}+n^{4}}\]

The value of \(H = A\cdot e\) and value of \(S = \frac{B}{C}\).Then find \(A+B+C\) .