A303352 - OEIS

%I #18 Apr 25 2018 03:33:26

%S 1,-2,4,-18,66,-230,832,-3118,11764,-44374,168476,-643974,2470506,

%T -9503946,36666736,-141824034,549717490,-2134650662,8303024092,

%U -32343942934,126161860886,-492703658930,1926278860624,-7538530620746,29529208903872,-115766389203370

%N Expansion of Product_{n>=1} 1/(1 + 4*x^n)^(1/2).

%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/2, g(n) = -4.

%H Seiichi Manyama, <a href="/A303352/b303352.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ c * (-4)^n / sqrt(Pi*n), where c = 1 / QPochhammer[-1/4]^(1/2) = 0.91806413264267465793225216525758518... - _Vaclav Kotesovec_, Apr 25 2018

%p seq(coeff(series(mul(1/(1+4*x^k)^(1/2), k = 1..n), x, n+1), x, n), n=0..40); # _Muniru A Asiru_, Apr 22 2018

%t nmax = 30; CoefficientList[Series[Product[1/(1 + 4*x^k)^(1/2), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 25 2018 *)

%Y Expansion of Product_{n>=1} 1/(1 + b^2*x^n)^(1/b): A081362 (b=1), this sequence (b=2), A303353 (b=3).

%Y Cf. A067855, A303350.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 22 2018