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 A233829 #20 Sep 08 2022 08:46:06
%S A233829 1,9,90,975,11160,132867,1629012,20430900,260907075,3381098545,
%T A233829 44352058608,587787511779,7858257798300,105855415586550,
%U A233829 1435361957277480,19576154604317304,268364706225271110,3695862686045572350,51108790709588823150
%N A233829 a(n) = 3*binomial(6*n+9,n)/(2*n+3).
%C A233829 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, r=9.
%H A233829 Vincenzo Librandi, <a href="/A233829/b233829.txt">Table of n, a(n) for n = 0..200</a>
%H A233829 J-C. Aval, <a href="http://arxiv.org/pdf/0711.0906v1.pdf">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
%H A233829 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233829 Wojciech Mlotkowski, <a href="http://www.math.uiuc.edu/documenta/vol-15/28.pdf">Fuss-Catalan Numbers in Noncommutative Probability</a>, Docum. Mathm. 15: 939-955.
%F A233829 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=6, r=9.
%F A233829 From _Ilya Gutkovskiy_, Sep 14 2018: (Start)
%F A233829 E.g.f.: 5F5(3/2,5/3,11/6,13/6,7/3; 1,11/5,12/5,13/5,14/5; 46656*x/3125).
%F A233829 a(n) ~ 3^(6*n+21/2)*4^(3*n+4)/(sqrt(Pi)*5^(5*n+19/2)*n^(3/2)). (End)
%t A233829 Table[3 Binomial[6 n + 9, n]/(2 n + 3), {n, 0, 30}]
%o A233829 (PARI) a(n) = 3*binomial(6*n+9,n)/(2*n+3);
%o A233829 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/3))^9+x*O(x^n)); polcoeff(B, n)}
%o A233829 (Magma) [3*Binomial(6*n+9, n)/(2*n+3): n in [0..30]];
%Y A233829 Cf. A000108, A002295, A212071, A212072, A212073, A130564, A233743, A233827, A233830.
%K A233829 nonn
%O A233829 0,2
%A A233829 _Tim Fulford_, Dec 16 2013