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%I #16 Nov 04 2021 15:09:08
%S 1,5,200,5125,177500,3952500,150715625,3185187500,112844843750,
%T 2783033593750,86330708203125,2019237027343750,72195817812500000,
%U 1591910699609375000,50158322275878906250,1322261581989501953125,39183430287559814453125,946961406814801025390625
%N Expansion of Product_{n>=1} (1 - (25*x)^n)^(-1/5).
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/5, g(n) = 25^n.
%H Seiichi Manyama, <a href="/A303136/b303136.txt">Table of n, a(n) for n = 0..500</a>
%F 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
%t CoefficientList[Series[1/QPochhammer[25*x]^(1/5), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 19 2018 *)
%t CoefficientList[Series[Product[(1-(25x)^n)^(-1/5),{n,20}],{x,0,20}],x] (* _Harvey P. Dale_, Nov 04 2021 *)
%Y Expansion of Product_{n>=1} (1 - ((b^2)*x)^n)^(-1/b): A000041 (b=1), A271235 (b=2), A271236 (b=3), A303135 (b=4), this sequence (b=5).
%Y Cf. A303132, A303154.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 19 2018
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