How do I just output A(0) using your code? My crude method is

solutions:= evalf(solve({SA,SB},{seq(A(k),k=0..n-2),seq(B(k),k=1..n-1)}));

eval(A(0), solutions);

Yes indeed.  Can maple find a general closed form solution as a function of n?

Yes indeed.  Can maple find a general closed form solution as a function of n?