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 A235340 #20 May 28 2025 14:19:12
%S A235340 1,10,155,2870,58565,1270752,28765650,671650110,16057800980,
%T A235340 391139588190,9672348219898,242182964452000,6127720969229265,
%U A235340 156431295179478200,4024231652469275640,104218796026870015374,2714941275486017847825
%N A235340 a(n) = 10*binomial(11*n+10,n)/(11*n+10).
%C A235340 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=10.
%H A235340 Vincenzo Librandi, <a href="/A235340/b235340.txt">Table of n, a(n) for n = 0..200</a>
%H A235340 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 A235340 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A235340 Elżbieta Liszewska and Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H A235340 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 A235340 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p=11, r=10.
%F A235340 From _Wolfdieter Lang_, Feb 15 2024: (Start)
%F A235340 a(n) = binomial(11*n + 9, n + 1)/(10*n + 9) which is instance k = 10 of c(k, n+1) given in a comment in A130564.
%F A235340 x*B(x), with the g.f. above named B(x), is the compositional inverse of y*(1 - y)^10, hence B(x)*(1 - x*B(x))^10 = 1.
%F A235340 G.f.: 11F10([10..20]/11, [11..20]/10; (11^11/10^10)*x) = (10/(11*x))*(1 - 10F9([-1,1,2,3,4,5,6,7,8,9]/11, [1,2,3,4,5,6,7,8,9]/10; (11^11/10^10)*x)).
%F A235340 (End)
%t A235340 Table[10 Binomial[11 n + 10, n]/(11 n + 10), {n, 0, 30}]
%o A235340 (PARI) a(n) = 10*binomial(11*n+10,n)/(11*n+10);
%o A235340 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/10))^10+x*O(x^n)); polcoeff(B, n)}
%o A235340 (Magma) [10*Binomial(11*n+10, n)/(11*n+10): n in [0..30]];
%Y A235340 Cf. A130564, A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235338, A235339.
%K A235340 nonn,easy
%O A235340 0,2
%A A235340 _Tim Fulford_, Jan 06 2014