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A346679 Expansion of Product_{k>=1} (1 + x^k*(1+x)) / (1 - x^k*(1+x)). 0

%I

%S 1,2,6,14,32,68,140,280,544,1034,1930,3544,6416,11472,20288,35532,

%T 61696,106304,181906,309362,523228,880576,1475424,2462302,4094682,

%U 6787588,11219504,18498094,30429502,49955706,81864400,133940690,218834842,357090226,582050680

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

%C Convolution of A160571 and A227681.

%F a(n) ~ 2*c * phi^(n+1) / sqrt(5), where phi = A001622 is the golden ratio and c = Product_{k>=2} (phi^k + 1 + 1/phi) / (phi^k - 1 - 1/phi) = 32.9911047431709572178149423384235021321790640826498395008790713974339...

%t nmax = 50; CoefficientList[Series[Product[(1+x^k*(1+x))/(1-x^k*(1+x)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A160571, A227681.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jul 31 2021

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Last modified February 6 17:34 EST 2023. Contains 360110 sequences. (Running on oeis4.)