%I #16 Apr 20 2018 08:41:44

%S 1,-4,-24,-1248,1632,-267136,-669440,-56925184,597165568,-19934894080,

%T 61831327744,-3209599664128,47593545383936,-840449808072704,

%U 8113679782510592,-350055154021040128,5703847053344768000,-57129722970675609600,704939718429511778304

%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="/A303131/b303131.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) ~ (-1)^n * exp(Pi*sqrt(n/24)) * 2^(4*n - 9/4) / (3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 20 2018

%t CoefficientList[Series[(2/QPochhammer[-1, 16*x])^(1/4), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 20 2018 *)

%Y Expansion of Product_{n>=1} (1 + ((b^2)*x)^n)^(-1/b): A081362 (b=1), A298993 (b=2), A303130 (b=3), this sequence (b=4), A303132 (b=5).

%Y Cf. A303124, A303135.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 19 2018