This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A303352 #18 Apr 25 2018 03:33:26
%S A303352 1,-2,4,-18,66,-230,832,-3118,11764,-44374,168476,-643974,2470506,
%T A303352 -9503946,36666736,-141824034,549717490,-2134650662,8303024092,
%U A303352 -32343942934,126161860886,-492703658930,1926278860624,-7538530620746,29529208903872,-115766389203370
%N A303352 Expansion of Product_{n>=1} 1/(1 + 4*x^n)^(1/2).
%C A303352 This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/2, g(n) = -4.
%H A303352 Seiichi Manyama, <a href="/A303352/b303352.txt">Table of n, a(n) for n = 0..1000</a>
%F A303352 a(n) ~ c * (-4)^n / sqrt(Pi*n), where c = 1 / QPochhammer[-1/4]^(1/2) = 0.91806413264267465793225216525758518... - _Vaclav Kotesovec_, Apr 25 2018
%p A303352 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 A303352 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 A303352 Expansion of Product_{n>=1} 1/(1 + b^2*x^n)^(1/b): A081362 (b=1), this sequence (b=2), A303353 (b=3).
%Y A303352 Cf. A067855, A303350.
%K A303352 sign
%O A303352 0,2
%A A303352 _Seiichi Manyama_, Apr 22 2018