OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=4.
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. Mathm. 15 (2010), 939-955.
FORMULA
G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, with p=11, r=4.
a(n) ~ 11^(11*n+7/2) / (2^(10*n+3) * 5^(10*n+9/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 13 2025
a(n) = A234871(n) *4*(2*n+1)/(11*n+4). - R. J. Mathar, Mar 18 2026
D-finite with recurrence 800*n *(10*n+1) *(5*n+1) *(10*n+3) *(5*n+2) *(2*n-1) *(5*n-2) *(10*n-3) *(5*n-1) *(10*n-1)*a(n) -11*(11*n-5) *(11*n+1) *(11*n-4) *(11*n+2) *(11*n-3) *(11*n+3) *(11*n-2) *(11*n-7) *(11*n-1) *(11*n-6)*a(n-1)=0. - R. J. Mathar, Mar 18 2026
MATHEMATICA
Table[4 Binomial[11 n + 4, n]/(11 n + 4), {n, 0, 40}] (* Vincenzo Librandi, Jan 01 2014 *)
PROG
(PARI) a(n) = 4*binomial(11*n+4, n)/(11*n+4);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/4))^4+x*O(x^n)); polcoeff(B, n)}
(Magma) [4*Binomial(11*n+4, n)/(11*n+4): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Jan 01 2014
STATUS
approved
