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