I'm already familiar with calculating the odds of getting a certain number of *specific individual results* when rolling an arbitrary number of dice (simple binomial distribution). But a fair amount of Google searching and working out numbers by hand hasn't led me to a general formula for calculating the odds of getting a certain *total* when rolling an arbitrary number of dice. (e.g. What are the odds of rolling a total of 17 or greater using four standard 6-sided dice?) This looks like some form of binomial expansion, but I'm drawing a blank putting it all together.

And I can always post a 15c implementation of the calculation, since that's the hot topic at the moment. ;)