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 A370709 #9 Feb 28 2024 18:02:47
%S A370709 1,2,2,20,6,108,148,776,-186,5964,-4,51032,-89700,512120,-1259416,
%T A370709 6406032,-19733434,78363148,-268823572,1047941688,-3800035916,
%U A370709 14327505832,-52766730600,199492430192,-746479735524,2811936761016,-10588174502568,40092283176560,-151796846803592
%N A370709 a(n) = 2^n * [x^n] Product_{k>=1} (1 + 2*x^k)^(1/2).
%F A370709 G.f.: Product_{k>=1} (1 + 2*(2*x)^k)^(1/2).
%F A370709 a(n) ~ (-1)^(n+1) * c * 4^n / n^(3/2), where c = QPochhammer(-1/2)^(1/2) / (2*sqrt(Pi)) = 0.31039710860287467176143051675437...
%t A370709 nmax = 30; CoefficientList[Series[Product[(1 + 2*x^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] * 2^Range[0, nmax]
%t A370709 nmax = 30; CoefficientList[Series[Product[(1 + 2*(2*x)^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x]
%t A370709 nmax = 30; CoefficientList[Series[Sqrt[QPochhammer[-2, x]/3], {x, 0, nmax}], x] * 2^Range[0, nmax]
%Y A370709 Cf. A032302, A370713.
%Y A370709 Cf. A075900, A298994, A300581, A304961, A327550.
%K A370709 sign
%O A370709 0,2
%A A370709 _Vaclav Kotesovec_, Feb 27 2024