2009 AIME II Problem 7

Define n !! to be n(n-2)(n-4) \ldots 3 \cdot 1 for n odd and n(n-2)(n-4) \ldots 4 \cdot 2 for n even. When \sum_{i=1}^{2009} \frac{(2 i-1) ! !}{(2 i) ! !}
is expressed as a fraction in lowest terms, its denominator is 2^{a} b with b odd.
Find \frac{a b}{10}.