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 A370749 #7 Feb 29 2024 10:47:34
%S A370749 1,2,6,28,70,300,892,3544,9990,43340,127988,546120,1651356,7227896,
%T A370749 22414008,99344944,312879302,1396285452,4486205892,20057934312,
%U A370749 65293087284,292353604136,963327294536,4308913730256,14340603113372,64059675491512,215075154021384,958968160741328
%N A370749 a(n) = 2^n * [x^n] Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^(1/4).
%F A370749 G.f.: Product_{k>=1} ((1 + 2*(2*x)^k)/(1 - 2*(2*x)^k))^(1/4).
%F A370749 a(n) ~ QPochhammer(-1, 1/2)^(1/4) * 4^n / (Gamma(1/4) * QPochhammer(1/2)^(1/4) * n^(3/4)).
%t A370749 nmax = 30; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 2^Range[0, nmax]
%t A370749 nmax = 30; CoefficientList[Series[Product[(1 + 2*(2*x)^k)/(1 - 2*(2*x)^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]
%Y A370749 Cf. A261584, A303346, A370750.
%Y A370749 Cf. A032302, A070933.
%Y A370749 Cf. A370736, A370732.
%K A370749 nonn
%O A370749 0,2
%A A370749 _Vaclav Kotesovec_, Feb 29 2024