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A233827 a(n) = 8*binomial(6*n+8,n)/(6*n+8).

%I A233827 #24 Nov 22 2024 08:26:47
%S A233827 1,8,76,800,8990,105672,1283464,15981504,202927725,2617624680,
%T A233827 34206162848,451872681728,6024664312030,80964348872400,
%U A233827 1095590286231120,14915165412813184,204140673966231870,2807362363541687280,38772186055550141700
%N A233827 a(n) = 8*binomial(6*n+8,n)/(6*n+8).
%C A233827 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, r=8.
%H A233827 Vincenzo Librandi, <a href="/A233827/b233827.txt">Table of n, a(n) for n = 0..200</a>
%H A233827 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 A233827 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233827 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 A233827 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=6, r=8.
%F A233827 From _Ilya Gutkovskiy_, Sep 14 2018: (Start)
%F A233827 E.g.f.: 5F5(4/3,3/2,5/3,11/6,13/6; 1,9/5,11/5,12/5,13/5; 46656*x/3125).
%F A233827 a(n) ~ 3^(6*n+15/2)*4^(3*n+5)/(sqrt(Pi)*5^(5*n+17/2)*n^(3/2)). (End)
%F A233827 D-finite with recurrence 5*n*(5*n+6)*(5*n+7)*(5*n+8)*(5*n+4)*a(n) -72*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(6*n+7)*a(n-1)=0. - _R. J. Mathar_, Nov 22 2024
%t A233827 Table[8 Binomial[6 n + 8, n]/(6 n + 8), {n, 0, 30}]
%o A233827 (PARI) a(n) = 8*binomial(6*n+8,n)/(6*n+8);
%o A233827 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(6/8))^8+x*O(x^n)); polcoeff(B, n)}
%o A233827 (Magma) [8*Binomial(6*n+8, n)/(6*n+8): n in [0..30]];
%Y A233827 Cf. A000108, A002295, A212071, A212072, A212073, A130564, A233743, A233829, A233830.
%K A233827 nonn
%O A233827 0,2
%A A233827 _Tim Fulford_, Dec 16 2013