Distribution of counts?

What is the distribution of counts that I can expect to see after 3 decks are dealt out of a 6 deck shoe? I expected to find the answer in Griffin (everything else is there, after all) but I could only find the numbers for single deck.

It seems like this could be solved combinatorially, or by simulation, but I'd prefer not to re-invent the wheel if the numbers are out there somewhere.

Thanks, but not quite what I'm looking for. I'm not looking for the number of hands that will be of a certain count, I'm looking for the probability distribution of the final count.

Consider this: I take a 6-deck shoe and shuffle randomly. I cut the shoe in half. Let the random variable X represent the total count of the first half of the shoe. What is the distribution of X? (Obviously E[X] = 0)

I have the whole series but I don't know where they are. Each book in the series is the count probability distributions for various levels of penetration and various numbers of decks.. When software came out I moved to that. You may want to contact either person and ask if it's what you are looking for. It may be. It was fairly comprehensive.