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 A370752 #7 Feb 29 2024 10:47:26
%S A370752 1,6,36,360,1998,18792,121176,1123632,7537860,72078174,510702408,
%T A370752 4896308088,35923749480,345406994280,2600934294816,24985346997888,
%U A370752 191735328374478,1838307293836560,14317601666954364,136953233511162840,1079293961918593800,10299943344889922832
%N A370752 a(n) = 3^n * [x^n] Product_{k>=1} ((1 + 3*x^k)/(1 - 3*x^k))^(1/3).
%C A370752 In general, if d > 1, m >= 1 and g.f. = Product_{k>=1} ((1 + d*x^k)/(1 - d*x^k))^(1/m), then a(n) ~ QPochhammer(-1, 1/d)^(1/m) * d^n / (Gamma(1/m) * QPochhammer(1/d)^(1/m) * n^(1 - 1/m)).
%F A370752 G.f.: Product_{k>=1} ((1 + 3*(3*x)^k)/(1 - 3*(3*x)^k))^(1/3).
%F A370752 a(n) ~ QPochhammer(-1, 1/3)^(1/3) * 9^n / (Gamma(1/3) * QPochhammer(1/3)^(1/3) * n^(2/3)).
%t A370752 nmax = 30; CoefficientList[Series[Product[(1 + 3*x^k)/(1 - 3*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 3^Range[0, nmax]
%t A370752 nmax = 30; CoefficientList[Series[Product[(1 + 3*(3*x)^k)/(1 - 3*(3*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
%Y A370752 Cf. A303390 (d=3,m=1), A370751 (d=3,m=2), A370752 (d=3,m=3).
%Y A370752 Cf. A261584 (d=2,m=1), A303346 (d=2,m=2), A370750 (d=2,m=3), A370749 (d=2,m=4).
%Y A370752 Cf. A015128 (d=1,m=1), A303307 (d=1,m=2), A303342 (d=1,m=3).
%Y A370752 Cf. A032308, A242587.
%Y A370752 Cf. A370712, A370710.
%K A370752 nonn
%O A370752 0,2
%A A370752 _Vaclav Kotesovec_, Feb 29 2024