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Expansion of Product_{k>=1} 1/(1 - 2*x^(k^2)).
1

%I #15 Aug 31 2017 02:55:06

%S 1,2,4,8,18,36,72,144,292,586,1172,2344,4696,9396,18792,37584,75186,

%T 150380,300764,601528,1203092,2406200,4812408,9624816,19249704,

%U 38499446,76998908,153997824,307995792,615991660,1231983352,2463966720,4927933732,9855867616

%N Expansion of Product_{k>=1} 1/(1 - 2*x^(k^2)).

%F a(n) = c * 2^n, where c = Product_{k>=2} 1/(1 - 2^(1-k^2)) = 1.1473740190706250791012378892728990358979800885299281286906257674366893358222...

%t nmax = 30; CoefficientList[Series[Product[1/(1 - 2*x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A001156, A070933.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 31 2017