OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r, n)/(n*p + r), where p=9, r=3.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
Thomas A. Dowling, Catalan Numbers Chapter 7
Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955.
FORMULA
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=3.
MATHEMATICA
Table[Binomial[9n+3, n]/(3n+1), {n, 0, 30}]
PROG
(PARI) a(n) = binomial(9*n+3, n)/(3*n+1);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^3)^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [Binomial(9*n+3, n)/(3*n+1): n in [0..30]];
(Sage) [binomial(9*n+3, n)/(3*n+1) for n in (0..30)] # G. C. Greubel, Feb 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 27 2013
STATUS
approved