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=2; also, g.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r.
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
a(n) = 2*binomial(11*n+1,n-1)/n for n>0, a(0)=1. - Bruno Berselli, Jan 19 2014
a(n) ~ 11^(11*n+3/2) / (4^(5*n+1) * 5^(10*n+5/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 13 2025
D-finite with recurrence +800*n *(10*n+1) *(5*n+1) *(10*n-7) *(5*n-3) *(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-9) *(11*n-3) *(11*n-8) *(11*n-2) *(11*n-7) *(11*n-1) *(11*n-6)*a(n-1)=0. - R. J. Mathar, Mar 18 2026
a(n) = A234869(n)*2*(10*n+3)/(3*(11*n+2)). - R. J. Mathar, Mar 18 2026
MATHEMATICA
Table[2 Binomial[11 n + 2, n]/(11 n + 2), {n, 0, 30}] (* Vincenzo Librandi, Jan 01 2014 *)
PROG
(PARI)
a(n) = 2*binomial(11*n+2, n)/(11*n+2)
for(n=0, 20, print(a(n))) \\ Sequence
(PARI)
{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/2))^2+x*O(x^n)); polcoeff(B, n)}
for (n=0, 20, print(a(n))) \\ Generating Function
(Magma) [2*Binomial(11*n+2, n)/(11*n+2): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014
(SageMath) [2*binomial(11*n+2, n)/(11*n+2) for n in range(20)] # F. Chapoton; Apr 29 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Jan 01 2014
STATUS
approved