The first, 26, terms of  the sequence Sum(a(n,k)^2,k=0...infinity) where a(n,\
    k) is the coefficient of



             Prod(1+x^(2^i+(-1)^i)+x^(2^(i+1)+(-1)^(i+1),i=0..n-1)



                                      are

[1, 3, 11, 45, 197, 863, 3841, 17077, 76337, 341509, 1531543, 6875493, 30907245
, 139056207, 626170877, 2821513905, 12721321649, 57385011073, 258973449155, 
1169162212701, 5280031906267, 23851817573737, 107774016006369, 487080358636849,
2201758109153721, 9954306718655255]


                          This took, 195.158, second.