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%I #28 Sep 08 2022 08:46:06
%S 1,6,63,812,11655,178794,2869685,47593176,809172936,14028048650,
%T 247039158366,4406956913268,79470057050020,1446283758823470,
%U 26529603944225670,489989612605050800,9104498753815680600,170073237411754811568,3192081704235788729043
%N a(n) = 3*binomial(8*n+6,n)/(4*n+3).
%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p = 8, r = 6.
%H Vincenzo Librandi, <a href="/A234465/b234465.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.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p = 8, r = 6.
%F O.g.f. A(x) = 1/x * series reversion (x/C(x)^6), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/6) is the o.g.f. for A007556. - _Peter Bala_, Oct 14 2015
%F D-finite with recurrence: 7*n*(7*n+4)*(7*n+1)*(7*n+5)*(7*n+2)*(7*n+6)*(7*n+3)*a(n) -128*(8*n+3)*(4*n-1)*(8*n+1)*(2*n+1)*(8*n-1)*(4*n+1)*(8*n+5)*a(n-1)=0. - _R. J. Mathar_, Feb 21 2020
%t Table[3 Binomial[8 n + 6, n]/(4 n + 3), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (PARI) a(n) = 3*binomial(8*n+6,n)/(4*n+3);
%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/3))^6+x*O(x^n)); polcoeff(B, n)}
%o (Magma) [3*Binomial(8*n+6, n)/(4*n+3): n in [0..30]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A000108, A007556, A234461, A234462, A234463, A234464, A234466, A234467, A230390, A007556, A069271, A118970, A212073, A233834, A234510, A234571, A235339.
%K nonn,easy
%O 0,2
%A _Tim Fulford_, Dec 26 2013
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