OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, 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=10, r=3.
MATHEMATICA
Table[3 Binomial[10 n + 3, n]/(10 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)
PROG
(PARI) a(n) = 3*binomial(10*n+3, n)/(10*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/3))^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(10*n+3, n)/(10*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 27 2013
STATUS
approved