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 A370327 #5 Feb 15 2024 11:43:22
%S A370327 1,3,39,801,22329,783963,33142959,1637118297,92464016913,
%T A370327 5874794703027,414582627839319,32165264232976977,2720659595107779081,
%U A370327 249128649448324321419,24549819503580405230751,2590147977759401893135497,291286776584800990966021281,34781064869030286562513208163
%N A370327 E.g.f.: exp(Sum_{k>=1} binomial(3*k,k) * x^k).
%F A370327 E.g.f.: exp(2*cos(arccos(1 - 27*x/2)/6) / sqrt(4 - 27*x) - 1).
%F A370327 a(n) ~ 3^(3*n - 1/3) * exp((3/2)^(4/3)*n^(1/3) - n - 5/6) * n^(n - 1/3) / 2^(2*n + 1/6).
%t A370327 CoefficientList[Series[Exp[Sum[Binomial[3*k, k]*x^k, {k, 1, 20}]], {x, 0, 20}], x] * Range[0, 20]!
%t A370327 CoefficientList[Series[Exp[2*Cos[ArcCos[1 - 27*x/2]/6] / Sqrt[4 - 27*x] - 1], {x, 0, 20}], x] * Range[0, 20]!
%Y A370327 Cf. A005809, A229451, A370055, A370326.
%K A370327 nonn
%O A370327 0,2
%A A370327 _Vaclav Kotesovec_, Feb 15 2024