A309044 Expansion of Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1)))^2.
1, 2, 1, 2, 0, -2, 3, 2, -1, -4, 0, -4, 5, 10, -3, -2, 0, -6, -1, -6, 3, 8, -8, -8, 9, 18, 1, 10, -8, -26, 11, 2, -1, 4, -8, -12, 5, 10, -11, -10, 8, 18, -1, 10, -13, -32, 8, 0, 9, 34, 1, 18, -8, -34, 27, 18, -17, -36, -8, -36, 29, 74, -35, -18, 8, -6, 7, 10, -13, -24
Offset: 0
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Mathematica
nmax = 69; CoefficientList[Series[Product[(1 + x^(2^k) - x^(2^(k + 1)))^2, {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x] nmax = 69; A[] = 1; Do[A[x] = (1 + x - x^2)^2 A[x^2] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]