A Weird Sum To infinity

Calculus Level 4

\[ \large \displaystyle \sum_{n=2}^{\infty} \dfrac{n^4 + 3n^2 + 10n + 10}{2^n (n^4+4)} \]

If the summation above can be written as \(\frac ab\) for coprime positive integer, find \(a(b+1) \).

Innovative solutions are welcome!
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