A235338 - OEIS

%I #13 Mar 29 2023 07:53:46

%S 1,8,116,2080,41650,892552,20027112,464550336,11050084695,

%T 268070745800,6607118937848,164979021222400,4164615224071926,

%U 106105019316578800,2724883054841727200,70462458864489354624,1833143662625459289495

%N 8*binomial(11*n+8,n)/(11*n+8).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=8.

%H Vincenzo Librandi, <a href="/A235338/b235338.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> [broken link]

%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, here p=11, r=8.

%t Table[8 Binomial[11 n + 8, n]/(11 n + 8), {n, 0, 30}]

%o (PARI) a(n) = 8*binomial(11*n+8, n)/(11*n+8);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/8))^8+x*O(x^n)); polcoeff(B, n)}

%o (Magma) [8*Binomial(11*n+8, n)/(11*n+8): n in [0..30]];

%Y Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235339, A235340.

%K nonn

%O 0,2

%A _Tim Fulford_, Jan 06 2014