This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A230388 #60 Jun 16 2025 08:49:40
%S A230388 1,1,11,176,3311,68211,1489488,33870540,793542167,19022318084,
%T A230388 464333035881,11502251937176,288417894029200,7306488667126803,
%U A230388 186719056586568660,4807757550367267056,124609430032127192295,3248403420844673986345
%N A230388 a(n) = binomial(11*n+1,n)/(11*n+1).
%C A230388 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=1. Interesting property when r=1, a(n+1,p,1) = a(n,p,p) for n>=0.
%C A230388 This is also instance k = 10 of the generalized Catalan family {C(k, n)}_{n>=0} given in a comment of A130564. - _Wolfdieter Lang_, Feb 05 2024
%H A230388 Vincenzo Librandi, <a href="/A230388/b230388.txt">Table of n, a(n) for n = 0..200</a>
%H A230388 J-C. Aval, <a href="http://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906 [math.CO], 2008.
%H A230388 J-C. Aval, <a href="http://dx.doi.org/10.1016/j.disc.2007.08.100">Multivariate Fuss-Catalan Numbers</a>, Discrete Math., 308 (2008), 4660-4669.
%H A230388 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A230388 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.
%H A230388 J.-C. Novelli, J.-Y. Thibon, <a href="http://arxiv.org/abs/1403.5962">Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions</a>, arXiv preprint arXiv:1403.5962, 2014
%H A230388 Wikipedia, <a href="http://en.wikipedia.org/wiki/Fuss-Catalan_numbers">Fuss-Catalan number</a>
%F A230388 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, with p=11, r=1.
%F A230388 From _Robert FERREOL_, Apr 01 2015: (Start)
%F A230388 a(n) = binomial(11*n,n)/(10*n+1) = A062993(n+9, 9).
%F A230388 a(0) = 1; a(n) = Sum_{i1+i2+..i11=n-1} a(i1)*a(i2)*...*a(i11) for n>=1.
%F A230388 (End)
%F A230388 O.g.f.: hypergeometric([1,...,10]/11,[2,...,9,11]/10,(11^11/10^10)*x). For the e.g.f. put an extra 1 = 10/10 into the second part. - _Wolfdieter Lang_, Feb 05 2024
%F A230388 a(n) ~ (11^11/10^10)^n*sqrt(11/(2*Pi*(10*n)^3)). - _Robert A. Russell_, Jul 15 2024
%F A230388 G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^21). - _Seiichi Manyama_, Jun 16 2025
%p A230388 seq(binomial(11*k+1,k)/(11*k+1),k=0..30); # _Robert FERREOL_, Apr 01 2015
%p A230388 n:=30:G:=series(RootOf(g = 1+x*g^11, g),x=0,n+1):seq(coeff(G,x,k),k=0..n); # _Robert FERREOL_, Apr 01 2015
%t A230388 Table[Binomial[11 n + 1, n]/(11 n + 1), {n, 0, 30}] (* _Vincenzo Librandi_, Jan 01 2014 *)
%o A230388 (PARI) a(n) = binomial(11*n+1,n)/(11*n+1);
%o A230388 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11))+x*O(x^n)); polcoeff(B, n)}
%o A230388 (Magma) [Binomial(11*n+1,n)/(11*n+1): n in [0..30]]; // _Vincenzo Librandi_, Jan 01 2014
%Y A230388 Cf. A234868-A234873, A130564.
%K A230388 nonn,easy
%O A230388 0,3
%A A230388 _Tim Fulford_, Jan 01 2014