# What series is this?

Calculus Level 4

$\large S=\frac 8{3!} - \frac{32}{5!} + \frac{128}{7!} - \frac{512}{9!} + \cdots$

If $S$ as defined above can be represented as $\alpha - \sin \beta$ for some positive integers $\alpha$ and $\beta$, then find $\alpha + 19 \beta -1$.

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