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A303125
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Expansion of Product_{n>=1} (1 + (25*x)^n)^(1/5).
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4
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1, 5, 75, 4500, 43125, 2765000, 55871875, 1876671875, 25128437500, 1495793359375, 28953471875000, 871257974609375, 18280647500000000, 596362168603515625, 14502797130615234375, 519397373566650390625, 8604439235863037109375
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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) = -1/5, g(n) = -25^n.
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LINKS
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FORMULA
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a(n) ~ 5^(2*n - 1/4) * exp(Pi*sqrt(n/15)) / (2^(8/5) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 19 2018
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MATHEMATICA
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CoefficientList[Series[(QPochhammer[-1, 25*x]/2)^(1/5), {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+(25*x)^k)^(1/5)))
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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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