[math-fun] Regular n-simplex inscribed in an n-cube

Consider the unit n-cube and a largest regular n-simplex -- by volume -- that can fit inside it. What is V(n), the n-dimensional volume of that simplex, as a function of n? I think the first three of these are V(1) = 1, V(2) = 2sqrt(3) - 3, and V(3) = 1/3. If this is too hard to calculate in general, maybe there is an asymptotic formula for V(n) ? --Dan