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A234571 a(n) = 4*binomial(10*n+8,n)/(5*n+4).

%I A234571 #22 Sep 08 2022 08:46:06
%S A234571 1,8,108,1776,32430,632016,12876864,270964320,5843355957,128462407840,
%T A234571 2868356980060,64869895026144,1482877843096650,34207542810153216,
%U A234571 795318309360948240,18617396126132233920,438423206616057162258,10379232525028947311160,246878659984195222962220
%N A234571 a(n) = 4*binomial(10*n+8,n)/(5*n+4).
%C A234571 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p = 10, r = 8.
%H A234571 Vincenzo Librandi, <a href="/A234571/b234571.txt">Table of n, a(n) for n = 0..200</a>
%H A234571 J-C. Aval, <a href="http://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
%H A234571 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A234571 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 A234571 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F A234571 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p = 10, r = 8.
%F A234571 O.g.f. A(x) = 1/x * series reversion (x/C(x)^8), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/8) is the o.g.f. for A059968. - _Peter Bala_, Oct 14 2015
%t A234571 Table[4 Binomial[10 n + 8, n]/(5 n + 4), {n, 0, 30}]
%o A234571 (PARI) a(n) = 4*binomial(10*n+8,n)/(5*n+4);
%o A234571 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/4))^8+x*O(x^n)); polcoeff(B, n)}
%o A234571 (Magma) [4*Binomial(10*n+8, n)/(5*n+4): n in [0..30]];
%Y A234571 Cf. A059968, A234525, A234526, A234527, A234528, A234529, A234570, A234573, A059968, A069271, A118970, A212073, A233834, A234465, A234510, A235339.
%K A234571 nonn,easy
%O A234571 0,2
%A A234571 _Tim Fulford_, Dec 28 2013