A Weird Sum To infinity

Calculus Level 4

n=2n4+3n2+10n+102n(n4+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 ab\frac ab for coprime positive integer, find a(b+1)a(b+1) .

Innovative solutions are welcome!
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