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%I #7 Aug 14 2019 22:18:57
%S 1,2,6,12,30,60,132,264,558,1116,2292,4584,9300,18600,37464,74928,
%T 150414,300828,602772,1205544,2413380,4826760,9658104,19316208,
%U 38641716,77283432,154585464,309170928,618379320,1236758640,2473592208,4947184416,9894519246,19789038492,39578377812
%N G.f. A(x) satisfies: A(x) = A(x^2) / (1 - 2*x).
%F G.f.: Product_{k>=0} 1/(1 - 2*x^(2^k)).
%t nmax = 34; A[_] = 1; Do[A[x_] = A[x^2]/(1 - 2 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t nmax = 34; CoefficientList[Series[Product[1/(1 - 2 x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%o (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
%Y Cf. A001316, A018819, A171238, A308986.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Aug 14 2019