\[\large \sum_{k=3}^{\infty}\frac{k}{\left \lfloor \frac{k}{2}\right \rfloor!}=Ae-B\]

The equation above holds true for positive integers \(A\) and \(B\). Find \(A+B\).

**Notation:** \(e \approx 2.718\) denotes the Euler's number.

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