Let me try to explain with an example:

In[249]:= Product[x - i, {i, 0, t - 1}]

Out[249]= (1 - t + x) Pochhammer[2 - t + x, -1 + t]

what I need is the expression in "Out[249]", this is what I mean by "closed expression". Look that the boundary I've used is an unapropriate bound to a Table or to a loop, but it's not to the function "Product". I'm looking for a function that would do the same thing as the function Product but instead of using the usual multiplication of real numbers, it uses the usual matrix product.

I'm sorry, I guess I've not been clear. I need to calculate (not only for display) G(t-1)xG(t-2)x...xG(2)xG(1) without setting any value to t. For instance, the product x(x-1)...*(x-t) is equal to Gamma(x+1)/Gamma(x-t). I want to find a closed expression that would depend on t.