No no Please not Double Factorials

Define \(n!!\) as the double factorial. If \(\displaystyle\sum_{i=1}^{2009} \frac{(2i-1)!!}{(2i)!!}\) is expressed as a fraction in lowest terms, its denominator is \(2^ab\) with \(b\) odd. Find \(\dfrac{ab}{10}\).

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