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 A303438 #25 Nov 25 2024 04:59:47
%S A303438 1,2,4,10,18,38,80,158,292,630,1260,2470,4922,9706,19392,41010,78466,
%T A303438 155494,318764,625670,1238854,2567666,5106208,10122522,20022960,
%U A303438 40082154,80027140,163330106,324201942,643489014,1306843568,2592220110,5081546084
%N A303438 Expansion of Product_{k>=1} ((1 + 2^k*x^k)/(1 - 2^k*x^k))^(1/2^k).
%C A303438 a(n) / 2^n tends to 1.2036... - _Vaclav Kotesovec_, Apr 25 2018
%H A303438 Seiichi Manyama, <a href="/A303438/b303438.txt">Table of n, a(n) for n = 0..3000</a>
%H A303438 Vaclav Kotesovec, <a href="/A303438/a303438.jpg">Graph - The asymptotic ratio</a>
%F A303438 G.f.: exp( Sum_{j>=1} ((-1)^j - 1) / (j*(1 - 1/(2^(j-1)*x^j))) ). - _Vaclav Kotesovec_, Apr 25 2018
%t A303438 nmax = 30; CoefficientList[Series[Product[((1 + 2^k*x^k)/(1 - 2^k*x^k))^(1/2^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 24 2018 *)
%t A303438 nmax = 30; CoefficientList[Series[Exp[Sum[((-1)^j - 1) / (j*(1 - 1/(2^(j - 1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 25 2018 *)
%o A303438 (PARI) my(N=66, x='x+O('x^N)); Vec(prod(k=1, N, ((1+2^k*x^k)/(1-2^k*x^k))^(1/2^k)))
%Y A303438 Cf. A015128, A303346, A303360, A303382, A303439.
%K A303438 nonn
%O A303438 0,2
%A A303438 _Seiichi Manyama_, Apr 24 2018