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I have difficulties to find an approximation formula (or bound from the below) for the following sum:

$ \sum_{k=1}^n\left( \frac{1}{35}\right)^{k-1}(n-k)!\left(k-\frac 32\right)!. $

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    I've use representation of $\beta$ function in terms of $\Gamma$ function. Now I got the following sum and I have no idea how to approximate it. $\Gamma(k-0.5)=(k-3/2)!$2011-12-27

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