Decreasing sequence numbers with first digit $9$ 
Find the sum of all positive integers whose digits (in base ten) form a strictly decreasing sequence with first digit $9$.

The method I thought of for solving this was very computational and it depended on a lot of casework. Is there a nicer way to solve this question?
Note that there are $\displaystyle\sum_{n=0}^{9} \binom{9}{n} = 2^9$ such numbers.

Here a simple way to compute it with haskell. The idea is to take all subsequences of "876543210", prepend "9", parse that as an integer and sum them all:
Prelude> (sum $ map (read.("9"++)) $ Data.List.subsequences "876543210")::Integer
23259261861

