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A303136
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Expansion of Product_{n>=1} (1 - (25*x)^n)^(-1/5).
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6
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1, 5, 200, 5125, 177500, 3952500, 150715625, 3185187500, 112844843750, 2783033593750, 86330708203125, 2019237027343750, 72195817812500000, 1591910699609375000, 50158322275878906250, 1322261581989501953125, 39183430287559814453125, 946961406814801025390625
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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) ~ exp(Pi*sqrt(2*n/15)) * 5^(2*n - 3/10) / (2^(7/5) * 3^(3/10) * n^(4/5)). - Vaclav Kotesovec, Apr 19 2018
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MATHEMATICA
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CoefficientList[Series[1/QPochhammer[25*x]^(1/5), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 19 2018 *)
CoefficientList[Series[Product[(1-(25x)^n)^(-1/5), {n, 20}], {x, 0, 20}], x] (* Harvey P. Dale, Nov 04 2021 *)
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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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