as I mentioned [here][1], [this][2] paper provides some theoretical insight (and a way to approximate the true value). 

The authors end up with an approximative series for the density. It is implemented in the function maxdd of the R-package **fBasics**. There are convenient functions *dmaxdd*, *pmaxdd* and *rmaxdd*. Calculating the Expected Drawdown should be easy. (to be honest, I found the paper as a reference provided on the help page of the functions mentioned above)

The function you are asking for would be **maxddStats**:

    require(fBasics)
    maxddStats(mu,sigma,t)


  [1]: http://quant.stackexchange.com/questions/6997/comparison-of-brownian-motion-expected-drawdown-and-simulated-results?rq=1
  [2]: http://alumnus.caltech.edu/~amir/drawdown-jrnl.pdf