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A303132
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Expansion of Product_{n>=1} (1 + (25*x)^n)^(-1/5).
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5
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1, -5, -50, -3875, 2500, -2046250, -12409375, -1087687500, 13232343750, -907225000000, 1545669140625, -362705679687500, 6007095839843750, -224713698632812500, 2118331116210937500, -226812683210205078125, 4765872641563720703125
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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.
In general, for h>=1, if g.f. = Product_{k>=1} (1 + (h^2*x)^k)^(-1/h), then a(n) ~ (-1)^n * exp(Pi*sqrt(n/(6*h))) * h^(2*n) / (2^(7/4) * 3^(1/4) * h^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 20 2018
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LINKS
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FORMULA
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a(n) ~ (-1)^n * exp(Pi*sqrt(n/30)) * 5^(2*n - 1/4) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 20 2018
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MATHEMATICA
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CoefficientList[Series[(2/QPochhammer[-1, 25*x])^(1/5), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 20 2018 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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