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3*binomial(11*n+3,n)/(11*n+3).
9

%I #17 Sep 08 2022 08:46:06

%S 1,3,36,595,11385,237006,5212064,119126865,2801765835,67365151700,

%T 1648369018296,40914062713953,1027625691201200,26069631471224820,

%U 667024542735629400,17193066926119888716,446028709678732029135,11636873606948476550895

%N 3*binomial(11*n+3,n)/(11*n+3).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=3.

%H Vincenzo Librandi, <a href="/A234869/b234869.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, with p=11, r=3.

%t Table[3 Binomial[11 n + 3, n]/(11 n + 3), {n, 0, 30}] (* _Vincenzo Librandi_, Jan 01 2014 *)

%o (PARI) a(n) = 3*binomial(11*n+3,n)/(11*n+3);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/3))^3+x*O(x^n)); polcoeff(B, n)}

%o (Magma) [3*Binomial(11*n+3,n)/(11*n+3): n in [0..30]]; // _Vincenzo Librandi_, Jan 01 2014

%Y Cf. A230388, A234868, A234870, A234871, A234872, A234873.

%K nonn

%O 0,2

%A _Tim Fulford_, Jan 01 2014