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A260916
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Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(Fibonacci(k)).
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8
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1, 2, 4, 10, 22, 48, 104, 220, 460, 954, 1956, 3976, 8026, 16084, 32032, 63440, 124974, 245008, 478204, 929452, 1799508, 3471396, 6673724, 12788976, 24433528, 46546738, 88432264, 167575474, 316768948, 597389576, 1124092476, 2110661644, 3955006820, 7396477224
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OFFSET
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0,2
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COMMENTS
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Convolution of A166861 and A261050.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Vaclav Kotesovec, Asymptotics of the Euler transform of Fibonacci numbers, arXiv:1508.01796 [math.CO], Aug 07 2015.
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FORMULA
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a(n) ~ phi^n / (2^(3/4) * 5^(1/8) * sqrt(Pi) * n^(3/4)) * exp(-1/5 + 2*5^(-1/4)*sqrt(2*n) + s), where s = 2 * Sum_{k>=1} phi^(2*k+1) / ((phi^(4*k+2) - phi^(2*k+1) - 1)*(2*k+1)) = 0.276751423987223411719438512082359840225908317... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^Fibonacci[k], {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A000045, A001622, A166861, A261050, A261519, A261520.
Sequence in context: A033497 A327471 A239075 * A192627 A275445 A075560
Adjacent sequences: A260913 A260914 A260915 * A260917 A260918 A260919
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Aug 18 2015
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STATUS
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approved
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