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 A327682 #34 May 06 2021 05:03:36
%S A327682 1,-1,1,-5,14,-40,122,-404,1362,-4608,15881,-55709,197402,-705114,
%T A327682 2539282,-9210196,33605471,-123262137,454268676,-1681305246,
%U A327682 6246544735,-23288217459,87096982499,-326680267261,1228547420236,-4631474743422,17499462106763,-66257720483935,251356773101419
%N A327682 Expansion of Product_{k>0} (-1+sqrt(1+4*x^k))/(2*x^k).
%H A327682 Seiichi Manyama, <a href="/A327682/b327682.txt">Table of n, a(n) for n = 0..1000</a>
%F A327682 a(n) ~ (-1)^n * c * 4^n / n^(3/2), where c = 1/(2*sqrt(Pi)) * Product_{k>=1} (-1 + sqrt(1 + 4*(-1/4)^k)) / (2*(-1/4)^k) = 0.5396673413761086071059510679780476790558662471136055... - _Vaclav Kotesovec_, May 06 2021
%t A327682 m = 28; CoefficientList[Series[Product[(-1 + Sqrt[1 + 4*x^k])/(2*x^k), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 06 2021 *)
%o A327682 (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (-1+sqrt(1+4*x^k))/(2*x^k)))
%o A327682 (PARI) N=66; x='x+O('x^N); Vec(prod(i=1, N, sum(j=0, N\i, (-1)^j*binomial(2*j, j)*x^(i*j)/(j+1))))
%Y A327682 Cf. A000108, A081362, A168491, A309867, A322204, A327683.
%K A327682 sign
%O A327682 0,4
%A A327682 _Seiichi Manyama_, Sep 22 2019