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 A293306 #24 Jul 19 2025 13:06:37
%S A293306 1,-1,1,-3,4,-5,6,-9,13,-16,20,-27,36,-44,54,-69,88,-107,130,-162,200,
%T A293306 -240,288,-351,426,-507,602,-723,864,-1019,1200,-1422,1681,-1968,2300,
%U A293306 -2700,3160,-3674,4266,-4965,5768,-6665,7692,-8892,10260,-11792,13536,-15552
%N A293306 Expansion of (eta(q)*eta(q^3))/eta(q^2)^2 in powers of q.
%H A293306 Seiichi Manyama, <a href="/A293306/b293306.txt">Table of n, a(n) for n = 0..10000</a>
%H A293306 Shane Chern, Dennis Eichhorn, Shishuo Fu, and James A. Sellers, <a href="https://arxiv.org/abs/2507.10965">Convolutive sequences, I: Through the lens of integer partition functions</a>, arXiv:2507.10965 [math.CO], 2025. See p. 15.
%F A293306 G.f.: Product_{i>0} (1 + Sum_{j>0} (-1)^j*j*q^(j*i)).
%F A293306 a(n) ~ (-1)^n * exp(2*Pi*sqrt(n)/3) / (6*n^(3/4)). - _Vaclav Kotesovec_, Oct 05 2017
%t A293306 nmax = 50; CoefficientList[Series[Product[(1 - x^k) * (1 - x^(3*k)) / (1 - x^(2*k))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 05 2017 *)
%Y A293306 Main diagonal of A293305.
%Y A293306 Cf. A122792.
%K A293306 sign
%O A293306 0,4
%A A293306 _Seiichi Manyama_, Oct 05 2017