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 A320098 #24 Feb 16 2025 08:33:56
%S A320098 1,-2,4,-10,18,-34,64,-110,188,-320,524,-846,1358,-2130,3308,-5102,
%T A320098 7750,-11674,17468,-25862,38022,-55558,80532,-116034,166284,-236784,
%U A320098 335416,-472868,663146,-925762,1286920,-1780962,2454792,-3370806,4610656,-6284090,8535868,-11554834
%N A320098 Expansion of Product_{k>0} 1/theta_3(q^(2*k-1)), where theta_3() is the Jacobi theta function.
%H A320098 Vaclav Kotesovec, <a href="/A320098/b320098.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)
%H A320098 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%F A320098 Convolution inverse of A320078.
%F A320098 Expansion of Product_{k>0} (eta(q^(2*k-1))*eta(q^(4*(2*k-1))))^2 / eta(q^(2*(2*k-1)))^5.
%t A320098 nmax = 50; CoefficientList[Series[1/Product[EllipticTheta[3, 0, x^(2*k-1)], {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 06 2018 *)
%t A320098 nmax = 50; CoefficientList[Series[Product[(1 + x^(2*j*(2*k - 1)))^2/((1 - x^((2*k - 1)*j))*(1 + x^((2*k - 1)*j))^3), {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 06 2018 *)
%o A320098 (PARI) q='q+O('q^80); Vec(1/prod(k=1,50, eta(q^(2*(2*k-1)))^5/( eta(q^(2*k-1))* eta(q^(4*(2*k-1))))^2 ) ) \\ _G. C. Greubel_, Oct 29 2018
%Y A320098 Cf. A000122, A320068, A320078.
%K A320098 sign
%O A320098 0,2
%A A320098 _Seiichi Manyama_, Oct 05 2018