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 A296045 #19 Jan 17 2024 09:45:42
%S A296045 1,1,3,13,55,231,981,4222,18351,80320,353453,1562364,6932185,30856541,
%T A296045 137725710,616190583,2762605791,12408541299,55825435656,251523510045,
%U A296045 1134741006825,5125453110196,23175983361270,104899547541255,475228898015025,2154737528486881,9777332125043577
%N A296045 a(n) = [x^n] Product_{k>=1} ((1 + x^(2*k-1))/(1 - x^(2*k)))^n.
%H A296045 G. C. Greubel, <a href="/A296045/b296045.txt">Table of n, a(n) for n = 0..500</a>
%F A296045 a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 - x^(4*k)))^n.
%F A296045 a(n) ~ c * d^n / sqrt(n), where d = 4.62579056836776492108784045382518984897... (see A192540) and c = 0.255113338880004277664416308115912337... - _Vaclav Kotesovec_, Dec 05 2017
%t A296045 Table[SeriesCoefficient[Product[((1 + x^(2 k - 1))/(1 - x^(2 k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]
%t A296045 Table[SeriesCoefficient[Product[((1 + x^k)/(1 - x^(4 k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]
%t A296045 Table[SeriesCoefficient[(2 (-x)^(1/8)/EllipticTheta[2, 0, Sqrt[-x]])^n, {x, 0, n}], {n, 0, 26}]
%t A296045 Table[(-1)^n * 2^n * SeriesCoefficient[1/(QPochhammer[-1, x]*QPochhammer[x^2])^n, {x, 0, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Oct 07 2020 *)
%t A296045 (* Calculation of constants {d,c}: *) Chop[{1/r, 4/Sqrt[Pi*(77/2 - 4*s*(-r*s)^(7/8) * Derivative[0, 0, 2][EllipticTheta][2, 0, Sqrt[-r*s]])]} /. FindRoot[{s == (2*(-r*s)^(1/8))/EllipticTheta[2, 0, Sqrt[-r*s]], 7*I*r + 2*(-r*s)^(7/8)*Sqrt[r*s] * Derivative[0, 0, 1][EllipticTheta][2, 0, Sqrt[-r*s]] == 0}, {r, 1/5}, {s, 2}, WorkingPrecision -> 70]] (* _Vaclav Kotesovec_, Jan 17 2024 *)
%Y A296045 Cf. A006950, A106337, A192540, A273225, A273226, A273228, A295832, A296043, A296044.
%K A296045 nonn
%O A296045 0,3
%A A296045 _Ilya Gutkovskiy_, Dec 03 2017