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, arXiv:0711.0906 [math.CO], 2007; 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
a(n) = 2*binomial(11*n+1,n-1)/n for n>0, a(0)=1. [Bruno Berselli, Jan 19 2014]
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
(Sage) [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