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Time-consuming series coefficients


Hi,

I have the following function from which I would like to extract the 
coefficient of z^{50}, and then expand the result as a series in u:

f[z_,u_] := Product[1 + u (Exp(zpq^{i - 1}) - 1), {i,50}]

where p=q=1/2.

The product from i=1 to 10 can be done in a reasonable amount of time, but 
anything larger takes far too long.

Does anyone have an idea of how to expand f[z,u] as a series quickly, or even 
to extract the coefficient of z^{50} some other way?

Thanks,

M. Archibald
University of the Witwatersrand



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