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Question: Solve a pair of recurrence relations

Question:Solve a pair of recurrence relations

lesshaste 28 Maple
rsolve
December 27 2012
2

How can I solve a pair of recurrence relations like this in maple 16?

 

{A(k)=1+((n-k-2)/n)*A(k+1)+(2/n)*B(k+1)+(k/n)*(A(0)), B(k)=1+((n-k-1)/n)*B(k+1)+(k/n)*A(0)}

I want to solve for A(0).
 
A(k) is defined for 0

As a simple example, if you set n=3 then you should get A(0) = 33/5 but my attempts to use 
rsolve don't even give me anything useful at all.
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