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A229963 a(n) = 11*binomial(10*n + 11, n)/(10*n + 11) .

%I A229963 #69 Sep 08 2022 08:46:06
%S A229963 1,11,165,2860,53900,1072797,22188859,472214600,10273141395,
%T A229963 227440759700,5107663394691,116068178638776,2664012608972000,
%U A229963 61668340817988135,1438101958237201950,33753007927148177360,796704536753910327114
%N A229963 a(n) = 11*binomial(10*n + 11, n)/(10*n + 11) .
%C A229963 Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r,n)/(n*p + r), where p = 10, r = 11.
%H A229963 Vincenzo Librandi, <a href="/A229963/b229963.txt">Table of n, a(n) for n = 0..200</a>
%H A229963 J-C. Aval, <a href="http://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906 [math.CO], 2007.
%H A229963 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 A229963 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A229963 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 A229963 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F A229963 G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 10, r = 11.
%F A229963 From _Peter Bala, Oct 16 2015: (Start)
%F A229963 O.g.f. A(x) = 1/x * series reversion (x*C(-x)^11), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. See cross-references for other Fuss-Catalan sequences with o.g.f. 1/x * series reversion (x*C(-x)^k), k = 3 through 11.
%F A229963 A(x)^(1/11) is the o.g.f. for A059968. (End)
%F A229963 D-finite with recurrence: 81*n*(9*n+11)*(9*n+4)*(3*n+2)*(9*n+8)*(9*n+10)*(3*n+1)*(9*n+5)*(9*n+7)*a(n) -800*(10*n+1)*(5*n+1)*(10*n+3)*(5*n+2)*(2*n+1)*(5*n+3)*(10*n+7)*(5*n+4)*(10*n+9)*a(n-1)=0. - _R. J. Mathar_, Feb 21 2020
%t A229963 Table[11/(10 n + 11) Binomial[10 n + 11, n], {n, 0, 40}] (* _Vincenzo Librandi_, Jan 10 2014 *)
%o A229963 (PARI) a(n) = 11*binomial(10*n+11,n)/(10*n+11);
%o A229963 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/11))^11+x*O(x^n)); polcoeff(B, n)}
%o A229963 (Magma) [11*Binomial(10*n+11,n)/(10*n+11) : n in [0..20]]; // _Vincenzo Librandi_, Jan 10 2014
%Y A229963 Cf. A000108, A059968, A234525, A234526, A234527, A234528, A234529, A234570, A234571, A234573.
%Y A229963 Cf. A000245 (k = 3), A006629 (k = 4), A196678 (k = 5), A233668 (k = 6), A233743 (k = 7), A233835 (k = 8), A234467 (k = 9), A232265 (k = 10).
%K A229963 nonn,easy
%O A229963 0,2
%A A229963 _Tim Fulford_, Oct 04 2013
%E A229963 Corrected by _Vincenzo Librandi_, Jan 10 2014