%I #15 Apr 20 2018 10:06:58
%S 1,4,104,1760,39520,590720,14285056,205151232,4596467200,75375073280,
%T 1504196046848,23673049726976,525315968712704,7912159583600640,
%U 158055039529779200,2726833423421800448,51889395654107463680,840470097284214292480,16765991910040314839040
%N Expansion of Product_{n>=1} (1 - (16*x)^n)^(-1/4).
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/4, g(n) = 16^n.
%H Seiichi Manyama, <a href="/A303135/b303135.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) ~ exp(sqrt(n/6)*Pi) * 2^(4*n - 33/16) / (3^(5/16) * n^(13/16)). - _Vaclav Kotesovec_, Apr 19 2018
%t CoefficientList[Series[1/QPochhammer[16*x]^(1/4), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 19 2018 *)
%Y Expansion of Product_{n>=1} (1 - ((b^2)*x)^n)^(-1/b): A000041 (b=1), A271235 (b=2), A271236 (b=3), this sequence (b=4), A303136 (b=5).
%Y Cf. A303131, A303153.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 19 2018