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 A234461 #43 Sep 08 2022 08:46:06
%S A234461 1,2,17,200,2728,40508,635628,10368072,174047640,2987139122,
%T A234461 52177566870,924548764752,16578073731752,300252605231600,
%U A234461 5484727796499708,100933398334075824,1869468985400220600,34823332479175275600,651947852922093741585
%N A234461 a(n) = binomial(8*n+2,n)/(4*n+1).
%C A234461 Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r,n)/(n*p + r), this is the case p = 8, r = 2.
%H A234461 Vincenzo Librandi, <a href="/A234461/b234461.txt">Table of n, a(n) for n = 0..200</a>
%H A234461 J-C. Aval, <a href="http://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906 [math.CO], 2007.
%H A234461 J-C. Aval, <a href="http://dx.doi.org/10.1016/j.disc.2007.08.100">Multivariate Fuss-Catalan Numbers</a>, Discrete Math., 308 (2008), 4660-4669.
%H A234461 Gi-Sang Cheon, S.-T. Jin, and L. W. Shapiro, <a href="https://doi.org/10.1016/j.laa.2015.03.015">A combinatorial equivalence relation for formal power series</a>, Linear Algebra and its Applications, Volume 491, 15 February 2016, Pages 123-137.
%H A234461 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A234461 Clemens Heuberger, Sarah J. Selkirk, and Stephan Wagner, <a href="https://arxiv.org/abs/2204.14023">Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo k</a>, arXiv:2204.14023 [math.CO], 2022.
%H A234461 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.
%H A234461 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F A234461 G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 8, r = 2.
%F A234461 a(n) = 2*binomial(8n+1,n-1)/n for n>0, a(0)=1. [_Bruno Berselli_, Jan 19 2014]
%F A234461 A(x^3) = 1/x * series reversion (x/C(x^3)^2), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/2) is the o.g.f. for A007556. - _Peter Bala_, Oct 14 2015
%t A234461 Table[Binomial[8 n + 2, n]/(4 n + 1), {n, 0, 30}]
%o A234461 (PARI) a(n) = binomial(8*n+2,n)/(4*n+1);
%o A234461 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^4)^2+x*O(x^n)); polcoeff(B, n)}
%o A234461 (Magma) [Binomial(8*n+2, n)/(4*n+1): n in [0..30]];
%Y A234461 Cf. A000108, A007556, A234462, A234463, A234464, A234465, A234466, A234467, A230390.
%K A234461 nonn,easy
%O A234461 0,2
%A A234461 _Tim Fulford_, Dec 26 2013