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 A054370 #19 Jan 09 2024 09:38:29
%S A054370 1,1,0,21,182,2093,23394,285383,3621150,47813367,650302814,9066061193,
%T A054370 128986881660,1866877313441,27417577343674,407771633368995,
%U A054370 6131640430397790,93096368350684720,1425633583562073228,21998953427963954547,341803226976420690600
%N A054370 Number of unlabeled asymmetric 7-ary cacti having n polygons.
%H A054370 Andrew Howroyd, <a href="/A054370/b054370.txt">Table of n, a(n) for n = 0..200</a>
%H A054370 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 A054370 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A054370 a(n) = (1/n)*(Sum_{d|n} mu(n/d)*binomial(7*d, d)) - 6*binomial(7*n, n)/(6*n+1) for n > 0. - _Andrew Howroyd_, May 02 2018
%t A054370 a[0] = 1;
%t A054370 a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[7#, #]&]/n - 6 Binomial[7n, n]/(6n + 1);
%t A054370 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jul 01 2018, after _Andrew Howroyd_ *)
%o A054370 (PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(7*d, d))/n - 6*binomial(7*n, n)/(6*n+1)) \\ _Andrew Howroyd_, May 02 2018
%Y A054370 Column k=7 of A303913.
%Y A054370 Cf. A054369, A054371.
%K A054370 nonn
%O A054370 0,4
%A A054370 _Simon Plouffe_
%E A054370 Terms a(11) and beyond from _Andrew Howroyd_, May 02 2018