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A303124
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Expansion of Product_{n>=1} (1 + (16*x)^n)^(1/4).
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4
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1, 4, 40, 1504, 10336, 387968, 5349632, 111442944, 1100563968, 36711258112, 493805416448, 9186633203712, 134635599806464, 2648342619422720, 43443234834350080, 938422838970810368, 11378951438668791808, 224791017150689574912, 4129154423023897411584
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OFFSET
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0,2
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COMMENTS
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This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/4, g(n) = -16^n.
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LINKS
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FORMULA
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a(n) ~ 2^(4*n - 17/8) * exp(sqrt(n/3)*Pi/2) / (3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 19 2018
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MATHEMATICA
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CoefficientList[Series[(QPochhammer[-1, 16*x]/2)^(1/4), {x, 0, 20}],
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+(16*x)^k)^(1/4)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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