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 A052394 #22 Jan 09 2024 10:54:23
%S A052394 1,1,4,10,44,197,1228,7692,52828,373636,2735952,20506258,156922676,
%T A052394 1221179926,9642496488,77092885016,623121750844,5085013101164,
%U A052394 41850600967984,347060754685888,2897800158952304,24344668688424333,205667187527660076,1746375819789491996,14898241072028602276
%N A052394 Number of unlabeled 4-ary cacti having n polygons.
%H A052394 Andrew Howroyd, <a href="/A052394/b052394.txt">Table of n, a(n) for n = 0..200</a>
%H A052394 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 A052394 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A052394 a(n) = (1/n)*(Sum_{d|n} phi(n/d)*binomial(4*d, d)) - 3*binomial(4*n, n)/(3*n+1) for n > 0. - _Andrew Howroyd_, May 02 2018
%F A052394 a(n) ~ 2^(8*n + 1/2) / (sqrt(Pi) * n^(5/2) * 3^(3*n + 3/2)). - _Vaclav Kotesovec_, Jul 17 2017
%t A052394 a[n_] := If[n == 0, 1, (Binomial[4*n, n]/(3*n + 1) + DivisorSum[n, Binomial[4*#, #]*EulerPhi[n/#]*Boole[# < n] & ])/n]; Table[a[n], {n, 0, 24}] (* _Jean-François Alcover_, Jul 17 2017 *)
%o A052394 (PARI) a(n) = if(n==0, 1, sumdiv(n, d, eulerphi(n/d)*binomial(4*d, d))/n - 3*binomial(4*n, n)/(3*n+1)) \\ _Andrew Howroyd_, May 02 2018
%Y A052394 Column k=4 of A303912.
%Y A052394 Cf. A054362, A052395.
%K A052394 nonn
%O A052394 0,3
%A A052394 _Simon Plouffe_
%E A052394 More terms from _Jean-François Alcover_, Jul 17 2017