cp's OEIS Frontend

A235339 a(n) = 9*binomial(11*n+9,n)/(11*n+9).

%I A235339 #17 May 28 2025 12:34:48
%S A235339 1,9,135,2460,49725,1072197,24163146,562311720,13409091540,
%T A235339 325949656825,8046743477058,201198155083200,5084704634041305,
%U A235339 129673310477725350,3332952595603387800,86250038091202771344,2245329811618166111985
%N A235339 a(n) = 9*binomial(11*n+9,n)/(11*n+9).
%C A235339 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p = 11, r = 9.
%H A235339 Vincenzo Librandi, <a href="/A235339/b235339.txt">Table of n, a(n) for n = 0..200</a>
%H A235339 J-C. 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 A235339 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A235339 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 A235339 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F A235339 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p = 11, r = 9.
%F A235339 O.g.f. A(x) = 1/x * series reversion (x/C(x)^9), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/9) is the o.g.f. for A230388. - _Peter Bala_, Oct 14 2015
%t A235339 Table[9 Binomial[11 n + 9, n]/(11 n + 9), {n, 0, 30}]
%o A235339 (PARI) a(n) = 9*binomial(11*n+9,n)/(11*n+9);
%o A235339 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/9))^9+x*O(x^n)); polcoeff(B, n)}
%o A235339 (Magma) [9*Binomial(11*n+9, n)/(11*n+9): n in [0..30]];
%Y A235339 Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235338, A235340, A069271, A118970, A212073, A230388, A233834, A234465, A234510, A234571.
%K A235339 nonn,easy
%O A235339 0,2
%A A235339 _Tim Fulford_, Jan 06 2014