%I #18 Sep 08 2022 08:46:06

%S 1,6,69,992,15990,276360,5006386,93817152,1803606255,35373572460,

%T 704995403541,14236901646240,290687378847684,5990903682047592,

%U 124463414269524000,2603845580096662656,54807372993836345589,1159856934027109448130,24663454505518980363102,526708243449729452311200,11291926596343014148087470

%N 2*binomial(9*n+6,n)/(3*n+2).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=6.

%H Vincenzo Librandi, <a href="/A234509/b234509.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=9, r=6.

%t Table[6 Binomial[9 n + 6, n]/(9 n + 6), {n, 0, 30}]

%o (PARI) a(n) = 2*binomial(9*n+6,n)/(3*n+2);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/2))^6+x*O(x^n)); polcoeff(B, n)}

%o (Magma) [2*Binomial(9*n+6, n)/(3*n+2): n in [0..30]];

%Y Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234510, A234513, A232265.

%K nonn

%O 0,2

%A _Tim Fulford_, Dec 27 2013