@acer For users, the following one may be better in some sense. 

eval(eval(foldl(uneval(seq), F(i, j, k), i = 1 .. Ri, j = 1 .. Rj, k = 1 .. Rk)));

Or equivalently, 

(eval@@2@foldl)(''seq'',F(i,j,k),i=1..Ri,j=1..Rj,k=1..Rk);

Since it is more direct than using _seq or S (or other dummy names), though I think that there is no essential difference for Maple between them. (But strangely, while eval(subs(...)) works, subs[eval](...) fails.)
John Fredsted's construction is simple as well, but for big (i.e., long) sequence, eval–foldl–seq version is faster in my computer.