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 A054422 #20 Jul 02 2025 16:01:59
%S A054422 1,1,0,3,10,54,222,1107,5346,27399,142770,764967,4170672,23140813,
%T A054422 130189302,741650172,4270501218,24825326196,145534796520,859627488963,
%U A054422 5112003992610,30586307195304,184023393204654,1112800162657899
%N A054422 Number of unlabeled asymmetric ternary cacti having n triangles.
%H A054422 Andrew Howroyd, <a href="/A054422/b054422.txt">Table of n, a(n) for n = 0..200</a>
%H A054422 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 A054422 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A054422 a(n) = (1/n)*(Sum_{d|n} mu(n/d)*binomial(3*d, d)) - 2*binomial(3*n, n)/(2*n+1) for n > 0. - _Andrew Howroyd_, May 02 2018
%t A054422 a[0] = 1; a[n_] := (1/n) Sum[MoebiusMu[n/d] Binomial[3d, d], {d, Divisors[n] } ] - 2 Binomial[3n, n]/(2n + 1);
%t A054422 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jul 24 2018, after _Andrew Howroyd_ *)
%o A054422 (PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(3*d, d))/n - 2*binomial(3*n, n)/(2*n+1)) \\ _Andrew Howroyd_, May 02 2018
%Y A054422 Column k=3 of A303913.
%Y A054422 Cf. A052393, A054423.
%K A054422 nonn,easy
%O A054422 0,4
%A A054422 _Simon Plouffe_, Mar 15 2000
%E A054422 More terms from _James Sellers_, Mar 16 2000