OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, r=10.
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, here p=6, r=10.
From Ilya Gutkovskiy, Sep 14 2018: (Start)
E.g.f.: 6F6(5/3,11/6,2,13/6,7/3,5/2; 1,11/5,12/5,13/5,14/5,3; 46656*x/3125).
a(n) ~ 3^(6*n+19/2)*4^(3*n+5)/(sqrt(Pi)*5^(5*n+19/2)*n^(3/2)). (End)
MATHEMATICA
Table[5 Binomial[6 n + 10, n]/(3 n + 5), {n, 0, 30}]
PROG
(PARI) a(n) = 5*binomial(6*n+10, n)/(3*n+5);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/5))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [5*Binomial(6*n+10, n)/(3*n+5): n in [0..30]];
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 16 2013
STATUS
approved