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 A234505 #35 Jan 10 2025 11:24:15
%S A234505 1,2,19,252,3885,65274,1159587,21421248,407337153,7920326700,
%T A234505 156753610013,3147328992080,63951322669065,1312575792628356,
%U A234505 27172514322677625,566707337222428800,11896007334177739113,251142622845893276190,5328891499524964282170
%N A234505 a(n) = 2*binomial(9*n+2,n)/(9*n+2).
%C A234505 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=2.
%H A234505 Vincenzo Librandi, <a href="/A234505/b234505.txt">Table of n, a(n) for n = 0..200</a>
%H A234505 J-C. Aval, <a href="https://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906 [math.CO], 2007; Discrete Math., 308 (2008), 4660-4669.
%H A234505 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A234505 Wojciech Mlotkowski, <a href="https://www.emis.de/journals/DMJDMV/vol-15/28.html">Fuss-Catalan Numbers in Noncommutative Probability</a>, Docum. Mathm. 15: 939-955.
%H A234505 Jun Yan, <a href="https://arxiv.org/abs/2501.01152">Lattice paths enumerations weighted by ascent lengths</a>, arXiv:2501.01152 [math.CO], 2025. See p. 7.
%H A234505 Sheng-liang Yang and Mei-yang Jiang, <a href="https://journal.lut.edu.cn/EN/abstract/abstract528.shtml">Pattern avoiding problems on the hybrid d-trees</a>, J. Lanzhou Univ. Tech., (China, 2023) Vol. 49, No. 2, 144-150. (in Mandarin)
%F A234505 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=2.
%F A234505 a(n) = 2*binomial(9n+1,n-1)/n for n>0, a(0)=1. [_Bruno Berselli_, Jan 19 2014]
%t A234505 Table[2 Binomial[9 n + 2, n]/(9 n + 2), {n, 0, 30}]
%o A234505 (PARI) a(n) = 2*binomial(9*n+2,n)/(9*n+2);
%o A234505 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/2))^2+x*O(x^n)); polcoeff(B, n)}
%o A234505 (Magma) [2*Binomial(9*n+2, n)/(9*n+2): n in [0..30]];
%Y A234505 Cf. A000108, A143554, A234506, A234507, A234508, A234509, A234510, A234513, A232265.
%K A234505 nonn
%O A234505 0,2
%A A234505 _Tim Fulford_, Dec 27 2013