OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r, n)/(n*p + r); this is the case p = 5, r = 6.
REFERENCES
C. H. Pah, M. R. Wahiddin, Combinatorial Interpretation of Raney Numbers and Tree Enumerations, Open Journal of Discrete Mathematics, 2015, 5, 1-9; http://www.scirp.org/journal/ojdm; http://dx.doi.org/10.4236/ojdm.2015.51001
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.
J-C. Aval, Multivariate Fuss-Catalan Numbers, 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.
Wikipedia, Fuss-Catalan number
FORMULA
G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, here p = 5, r = 6.
From _Peter Bala, Oct 16 2015: (Start)
O.g.f. A(x) = 1/x * series reversion (x*C(-x)^6), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. See cross-references for other Fuss-Catalan sequences with o.g.f. 1/x * series reversion (x*C(-x)^k), k = 3 through 11.
A(x)^(1/6) is the o.g.f. for A002294. (End)
MATHEMATICA
Table[6 Binomial[5 n + 6, n]/(5 n + 6), {n, 0, 30}]
PROG
(PARI) a(n) = 6*binomial(5*n+6, n)/(5*n+6);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/6))^6+x*O(x^n)); polcoeff(B, n)}
(Magma) [6*Binomial(5*n+6, n)/(5*n+6): n in [0..30]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Tim Fulford, Dec 14 2013
STATUS
approved