1      2       4        8          16         
   S = --- + ----- + ----- + ------- + ---------- + ..... 
        2      5       41     3,281    21,523,361              

Each term n is as follows:

Numerator = 2^(n-1)

Denominator = (1 + 3^(2^(n-1))) / 2

This is basically a simplification of what Mindy wrote in a previous comment (thanks!).