A309728 G.f. A(x) satisfies: A(x) = A(x^2) / (1 - 2*x).
1, 2, 6, 12, 30, 60, 132, 264, 558, 1116, 2292, 4584, 9300, 18600, 37464, 74928, 150414, 300828, 602772, 1205544, 2413380, 4826760, 9658104, 19316208, 38641716, 77283432, 154585464, 309170928, 618379320, 1236758640, 2473592208, 4947184416, 9894519246, 19789038492, 39578377812
Offset: 0
Keywords
Programs
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Mathematica
nmax = 34; A[] = 1; Do[A[x] = A[x^2]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] nmax = 34; CoefficientList[Series[Product[1/(1 - 2 x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
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PARI
seq(n)=Vec(1/prod(k=0, logint(n,2), 1 - 2*x^(2^k) + O(x*x^n))) \\ Andrew Howroyd, Aug 14 2019
Formula
G.f.: Product_{k>=0} 1/(1 - 2*x^(2^k)).