# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a233829 Showing 1-1 of 1 %I A233829 #20 Sep 08 2022 08:46:06 %S A233829 1,9,90,975,11160,132867,1629012,20430900,260907075,3381098545, %T A233829 44352058608,587787511779,7858257798300,105855415586550, %U A233829 1435361957277480,19576154604317304,268364706225271110,3695862686045572350,51108790709588823150 %N A233829 a(n) = 3*binomial(6*n+9,n)/(2*n+3). %C A233829 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, r=9. %H A233829 Vincenzo Librandi, Table of n, a(n) for n = 0..200 %H A233829 J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669. %H A233829 Thomas A. Dowling, Catalan Numbers Chapter 7 %H A233829 Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955. %F A233829 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=6, r=9. %F A233829 From _Ilya Gutkovskiy_, Sep 14 2018: (Start) %F A233829 E.g.f.: 5F5(3/2,5/3,11/6,13/6,7/3; 1,11/5,12/5,13/5,14/5; 46656*x/3125). %F A233829 a(n) ~ 3^(6*n+21/2)*4^(3*n+4)/(sqrt(Pi)*5^(5*n+19/2)*n^(3/2)). (End) %t A233829 Table[3 Binomial[6 n + 9, n]/(2 n + 3), {n, 0, 30}] %o A233829 (PARI) a(n) = 3*binomial(6*n+9,n)/(2*n+3); %o A233829 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/3))^9+x*O(x^n)); polcoeff(B, n)} %o A233829 (Magma) [3*Binomial(6*n+9, n)/(2*n+3): n in [0..30]]; %Y A233829 Cf. A000108, A002295, A212071, A212072, A212073, A130564, A233743, A233827, A233830. %K A233829 nonn %O A233829 0,2 %A A233829 _Tim Fulford_, Dec 16 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE