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 A052393 #20 Jan 09 2024 09:39:38
%S A052393 1,1,3,6,19,57,258,1110,5475,27429,143379,764970,4173906,23140816,
%T A052393 130205922,741650802,4270593219,24825326199,145535320383,859627488966,
%U A052393 5112006997539,30586307211945,184023410798910,1112800162657902,6760426635625170
%N A052393 Number of unlabeled ternary cacti having n triangles.
%H A052393 Andrew Howroyd, <a href="/A052393/b052393.txt">Table of n, a(n) for n = 0..200</a>
%H A052393 Miklos Bona, Michel Bousquet, Gilbert Labelle, and Pierre Leroux, <a href="https://doi.org/10.1006/aama.1999.0665">Enumeration of m-ary cacti</a>, Advances in Applied Mathematics, 24 (2000), 22-56.
%H A052393 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A052393 a(n) = (1/n)*(Sum_{d|n} phi(n/d)*binomial(3*d, d)) - 2*binomial(3*n, n)/(2*n+1) for n > 0. - _Andrew Howroyd_, May 02 2018
%F A052393 a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi) * 2^(2*n + 2) * n^(5/2)). - _Vaclav Kotesovec_, Jul 17 2017
%t A052393 a[n_] := If[n == 0, 1, (Binomial[3*n, n]/(2*n+1) + DivisorSum[n, Binomial[ 3*#, #]*EulerPhi[n/#]*Boole[# < n]&])/n]; Table[a[n], {n, 0, 24}] (* _Jean-François Alcover_, Jul 17 2017 *)
%o A052393 (PARI) a(n) = if(n==0, 1, sumdiv(n, d, eulerphi(n/d)*binomial(3*d, d))/n - 2*binomial(3*n, n)/(2*n+1)) \\ _Andrew Howroyd_, May 02 2018
%Y A052393 Column k=3 of A303912.
%Y A052393 Cf. A054422, A054423.
%K A052393 nonn
%O A052393 0,3
%A A052393 _Simon Plouffe_
%E A052393 More terms from _Jean-François Alcover_, Jul 17 2017