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 A233667 #26 Nov 29 2024 23:50:40
%S A233667 1,10,85,700,5750,47502,395560,3321120,28102425,239503550,2054455634,
%T A233667 17726454200,153757722300,1340045361750,11729338225200,
%U A233667 103068670351552,908923976461140,8041606944709800,71359997110169625,634978885837495500,5664526697522326590
%N A233667 a(n) = 5*binomial(4*n+10,n)/(2*n+5).
%C A233667 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=4, r=10.
%H A233667 Vincenzo Librandi, <a href="/A233667/b233667.txt">Table of n, a(n) for n = 0..200</a>
%H A233667 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 A233667 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233667 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 A233667 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=4, r=10.
%F A233667 From _Ilya Gutkovskiy_, Sep 14 2018: (Start)
%F A233667 E.g.f.: 4F4(5/2,11/4,3,13/4; 1,11/3,4,13/3; 256*x/27).
%F A233667 a(n) ~ 5*2^(8*n+39/2)/(sqrt(Pi)*3^(3*n+21/2)*n^(3/2)). (End)
%t A233667 Table[5 Binomial[4 n + 10, n]/(2 n + 5), {n, 0, 30}]
%o A233667 (PARI) a(n) = 5*binomial(4*n+10,n)/(2*n+5);
%o A233667 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/5))^10+x*O(x^n)); polcoeff(B, n)}
%o A233667 (Magma) [5*Binomial(4*n+10,n)/(2*n+5): n in [0..30]];
%Y A233667 Cf. A000108, A002293, A069271, A006632, A196678, A006633, A233658, A233666, A006634, A006635.
%K A233667 nonn,easy
%O A233667 0,2
%A A233667 _Tim Fulford_, Dec 14 2013