What are the total number of genetic combinations in human offspring?

Well, look at it this way.
You got 23 chromosome from each parent.
There are 2^23 variations in the chromosome a mother gives, and the same number from the father.
2^23 is 8388608.
So, there can be 8388608^2 different children genetic make up from the same set of parents. That is already 70 trillion (in the short count) 70*10^12.

Now, there is the possibility that one parent would have two chromosome that are identical, or that parents would have a similar pair, so the number may be a bit less in some circumstances.

Now, we have to look at how many different chromosomes there are in the human population already, the existing set. And add to that the mutations, those that already have increased the set of existing chromosomes from the relatively small set that existed in a much smaller population one million years ago, and those that can still occur, given that more people means more possibility for "let's try this" variations and mutations.

The numbers quickly go totally out of hand.
There are probably more variations possible than there are atoms in the observable universe (which is estimated at around 10^80).