Question: Calculation of symbolic complex sequences

I am trying to calculate a symbolic complex sequence given in the below picture: 

I have written the following code; however, it is not efficient at all and it takes a very long time to calculate even the first elements of the sequences. Can anyone please help me fix that or suggest an efficient way of doing such calculation in complex domain? Any help is appreciated. Thanks

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d(0):=1+1I;

M(0):=1-2I;

for k from 0 to 3 do u(k):=-d(k)/M(k);p(k+1):=M__s*u(k)+d__s;d(k+1):=d(k)+gamma*p(k+1)/(nu+abs(u(k))^2);M(k+1):=M(k)+gamma*p(k+1)*conjugate(u(k))/(nu+abs(u(k))^2);od;

 

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