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 A268498 #14 Nov 07 2019 04:46:57
%S A268498 1,1,0,3,-1,3,3,3,0,4,12,0,9,-3,21,12,17,-3,33,0,33,36,36,27,21,52,24,
%T A268498 90,72,99,24,138,21,207,0,261,149,267,45,333,174,339,174,345,411,654,
%U A268498 330,456,657,535,684,483,1233,489,1353,882,1803,720,1902,756
%N A268498 Expansion of Product_{k>=1} ((1 + 2*x^k) / (1 + x^k)).
%C A268498 It appears that this sequence contains only finitely many nonpositive terms, namely at indices {2, 4, 8, 11, 13, 17, 19, 34}. - _Gus Wiseman_, Jan 23 2019
%H A268498 Vaclav Kotesovec, <a href="/A268498/b268498.txt">Table of n, a(n) for n = 0..5000</a>
%H A268498 Vaclav Kotesovec, <a href="/A268498/a268498.jpg">Graph - The asymptotic ratio</a>
%F A268498 a(n) ~ c^(1/4) * exp(sqrt(c*n)) / (2*sqrt(3*Pi)*n^(3/4)), where c = Pi^2/3 + 2*log(2)^2 + 4*polylog(2, -1/2) = 2.4571173338382709125... .
%F A268498 a(n) = Sum_{k = 0...n} (-1)^k * A133121(n,k). - _Gus Wiseman_, Jan 23 2019
%F A268498 G.f.: Product_{k>=1} (1 - Sum_{j>=1} (-1)^j * x^(k*j)). - _Ilya Gutkovskiy_, Nov 06 2019
%t A268498 nmax = 100; CoefficientList[Series[Product[(1+2*x^k)/(1+x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A268498 Cf. A032302, A264686, A268499, A268500.
%Y A268498 Cf. A006951, A100471, A133121.
%K A268498 sign
%O A268498 0,4
%A A268498 _Vaclav Kotesovec_, Feb 06 2016