OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=8, r=10.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Jean-Christophe Aval, Multivariate Fuss-Catalan Numbers, Discrete Math., Vol. 308, No. 20 (2008), 4660-4669; arXiv preprint, arXiv:0711.0906 [math.CO], 2007.
Thomas A. Dowling, Catalan Numbers, Chapter 7 of Applications of discrete mathematics, John G. Michaels and Kenneth H. Rosen (eds.), McGraw-Hill, New York, 1991. [Wayback Machine link]
Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Math. 15 (2010), 939-955.
FORMULA
G.f. satisfies: A(x) = (1 + x*A(x)^(p/r))^r, where p=8, r=10.
a(n) ~ 5 * 2^(24*n+29) / (7^(7*n+21/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 14 2025
MATHEMATICA
Table[5 Binomial[8 n + 10, n]/(4 n + 5), {n, 0, 30}]
PROG
(PARI) a(n) = 5*binomial(8*n+10, n)/(4*n+5);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/5))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [5*Binomial(8*n+10, n)/(4*n+5): n in [0..30]];
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 28 2013
STATUS
approved