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%I #30 Sep 08 2022 08:46:06
%S 1,8,68,616,5850,57536,581196,5995184,62891499,668922800,7197169980,
%T 78195588168,856708896784,9454328800896,104997940138300,
%U 1172624772468960,13161188646791865,148375147999406328,1679436658449372744,19078164706488179600
%N a(n) = 8*binomial(5*n + 8, n)/(5*n + 8).
%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=5, r=8.
%H Vincenzo Librandi, <a href="/A233736/b233736.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=5, r=8.
%F From _Ilya Gutkovskiy_, Sep 14 2018: (Start)
%F E.g.f.: 5F5(8/5,9/5,2,11/5,12/5; 1,9/4,5/2,11/4,3; 3125*x/256).
%F a(n) ~ 5^(5*n+15/2)/(sqrt(Pi)*2^(8*n+29/2)*n^(3/2)). (End)
%t Table[8 Binomial[5 n + 8, n]/(5 n + 8), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 16 2013 *)
%o (PARI) a(n) = 8*binomial(5*n+8,n)/(5*n+8);
%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/8))^8+x*O(x^n)); polcoeff(B, n)}
%o (Magma) [8*Binomial(5*n+8,n)/(5*n+8): n in [0..30]]; // _Vincenzo Librandi_, Dec 16 2013
%Y Cf. A000108, A002294, A118969, A143546, A118971, A233668, A233669, A233737, A233738.
%K nonn
%O 0,2
%A _Tim Fulford_, Dec 15 2013
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