%I #19 Sep 08 2022 08:46:06
%S 1,4,38,468,6545,98728,1566040,25747128,434824104,7498246100,
%T 131477423220,2337053822012,42016842044268,762702138530080,
%U 13959382918289880,257323577200329904,4773171937236245400,89028543731246186400,1668706597425638149302
%N Binomial(8*n+4,n)/(2*n+1).
%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=8, r=4.
%H Vincenzo Librandi, <a href="/A234463/b234463.txt">Table of n, a(n) for n = 0..200</a>
%H 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 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H 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 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=8, r=4.
%t Table[Binomial[8 n + 4, n]/(2 n + 1), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (PARI) a(n) = binomial(8*n+4,n)/(2*n+1);
%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^2)^4+x*O(x^n)); polcoeff(B, n)}
%o (Magma) [Binomial(8*n+4, n)/(2*n+1): n in [0..30]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A000108, A007556, A234461, A234462, A234464, A234465, A234466, A234467, A230390.
%K nonn
%O 0,2
%A _Tim Fulford_, Dec 26 2013