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A234868 a(n) = 2*binomial(11*n+2,n)/(11*n+2).

%I A234868 #24 Sep 08 2022 08:46:06
%S A234868 1,2,23,374,7095,146916,3219216,73386170,1722567143,41352865400,
%T A234868 1010607195741,25058477434562,628845572227600,15941429819185752,
%U A234868 407626109449551300,10501154649486399096,272294680440574235015,7101160966497659412010,186134223613500403098396
%N A234868 a(n) = 2*binomial(11*n+2,n)/(11*n+2).
%C A234868 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 A234868 Vincenzo Librandi, <a href="/A234868/b234868.txt">Table of n, a(n) for n = 0..200</a>
%H A234868 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 A234868 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 A234868 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 A234868 a(n) = 2*binomial(11*n+1,n-1)/n for n>0, a(0)=1. [_Bruno Berselli_, Jan 19 2014]
%t A234868 Table[2 Binomial[11 n + 2, n]/(11 n + 2), {n, 0, 30}] (* _Vincenzo Librandi_, Jan 01 2014 *)
%o A234868 (PARI)
%o A234868 a(n) = 2*binomial(11*n+2,n)/(11*n+2)
%o A234868 for(n=0,20, print(a(n))) \\ Sequence
%o A234868 (PARI)
%o A234868 {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/2))^2+x*O(x^n)); polcoeff(B, n)}
%o A234868 for (n=0,20, print(a(n))) \\ Generating Function
%o A234868 (Magma) [2*Binomial(11*n+2,n)/(11*n+2): n in [0..30]]; // _Vincenzo Librandi_, Jan 01 2014
%o A234868 (Sage) [2*binomial(11*n+2,n)/(11*n+2) for n in range(20)] # _F. Chapoton_; Apr 29 2020
%Y A234868 Cf. A230388, A234869, A234870, A234871, A234872, A234873.
%K A234868 nonn
%O A234868 0,2
%A A234868 _Tim Fulford_, Jan 01 2014