A234868 - OEIS

%I #24 Sep 08 2022 08:46:06

%S 1,2,23,374,7095,146916,3219216,73386170,1722567143,41352865400,

%T 1010607195741,25058477434562,628845572227600,15941429819185752,

%U 407626109449551300,10501154649486399096,272294680440574235015,7101160966497659412010,186134223613500403098396

%N a(n) = 2*binomial(11*n+2,n)/(11*n+2).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=2; also, g.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r.

%H Vincenzo Librandi, <a href="/A234868/b234868.txt">Table of n, a(n) for n = 0..200</a>

%H Jean-Christophe Aval, <a href="https://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906 [math.CO], 2007; Discrete Math., 308 (2008), 4660-4669.

%H Thomas A. Dowling, <a href="https://web.archive.org/web/20170918200322/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 a(n) = 2*binomial(11*n+1,n-1)/n for n>0, a(0)=1. [_Bruno Berselli_, Jan 19 2014]

%t Table[2 Binomial[11 n + 2, n]/(11 n + 2), {n, 0, 30}] (* _Vincenzo Librandi_, Jan 01 2014 *)

%o (PARI)

%o a(n) = 2*binomial(11*n+2,n)/(11*n+2)

%o for(n=0,20, print(a(n))) \\ Sequence

%o (PARI)

%o {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/2))^2+x*O(x^n)); polcoeff(B, n)}

%o for (n=0,20, print(a(n))) \\ Generating Function

%o (Magma) [2*Binomial(11*n+2,n)/(11*n+2): n in [0..30]]; // _Vincenzo Librandi_, Jan 01 2014

%o (Sage) [2*binomial(11*n+2,n)/(11*n+2) for n in range(20)] # _F. Chapoton_; Apr 29 2020

%Y Cf. A230388, A234869, A234870, A234871, A234872, A234873.

%K nonn

%O 0,2

%A _Tim Fulford_, Jan 01 2014