OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=2.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
J-C. 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.
Sheng-liang Yang and Mei-yang Jiang, Pattern avoiding problems on the hybrid d-trees, J. Lanzhou Univ. Tech., (China, 2023) Vol. 49, No. 2, 144-150. (in Mandarin)
FORMULA
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=2.
a(n) = 2*binomial(9n+1,n-1)/n for n>0, a(0)=1. [Bruno Berselli, Jan 19 2014]
MATHEMATICA
Table[2 Binomial[9 n + 2, n]/(9 n + 2), {n, 0, 30}]
PROG
(PARI) a(n) = 2*binomial(9*n+2, n)/(9*n+2);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/2))^2+x*O(x^n)); polcoeff(B, n)}
(Magma) [2*Binomial(9*n+2, n)/(9*n+2): n in [0..30]];
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 27 2013
STATUS
approved