as I mentioned herehere, this 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)