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a(n) ~ phi^(n+1), where phi =A001622= (1+sqrt(5))/2 is the golden ratio. -Vaclav Kotesovec,Sep 22 2019

nmax = 40; CoefficientList[Series[Product[1/(1 - x^k/(1 - x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x] (*Vaclav Kotesovec,Sep 22 2019 *)

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G

G

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proposed

Expansion of1/Product_{k>=1}1/(1-x^k/(1-x^(2*k))).

(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, 1-x^k/(1-x^(2*k))))