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 A054369 #20 Jan 09 2024 08:48:18
%S A054369 1,1,7,28,231,2100,23884,285390,3626295,47813815,650367788,9066061200,
%T A054369 128987761308,1866877313448,27417589615234,407771633434368,
%U A054369 6131640607962135,93096368350684727,1425633586192690945,21998953427963954554,341803227016091180620
%N A054369 Number of unlabeled 7-ary cacti having n polygons.
%H A054369 Andrew Howroyd, <a href="/A054369/b054369.txt">Table of n, a(n) for n = 0..200</a>
%H A054369 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 A054369 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A054369 a(n) = (1/n)*(Sum_{d|n} phi(n/d)*binomial(7*d, d)) - 6*binomial(7*n, n)/(6*n+1) for n > 0. - _Andrew Howroyd_, May 02 2018
%F A054369 a(n) ~ 7^(7*n + 1/2) / (2 * sqrt(3*Pi) * n^(5/2) * 6^(6*n + 1)). - _Vaclav Kotesovec_, Jul 17 2017
%t A054369 a[n_] := If[n == 0, 1, (Binomial[7*n, n]/(6 n + 1) + DivisorSum[n, Binomial[7*#, #]*EulerPhi[n/#]*Boole[# < n] & ])/n]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jul 17 2017 *)
%o A054369 (PARI) a(n) = if(n==0, 1, sumdiv(n, d, eulerphi(n/d)*binomial(7*d, d))/n - 6*binomial(7*n, n)/(6*n+1)) \\ _Andrew Howroyd_, May 02 2018
%Y A054369 Column k=7 of A303912.
%Y A054369 Cf. A054370, A054371.
%K A054369 nonn
%O A054369 0,3
%A A054369 _Simon Plouffe_
%E A054369 More terms from _Jean-François Alcover_, Jul 17 2017