OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=7, r=10.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, 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
72*n*(6*n+5)*(3*n+5)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) -7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+9)*(7*n+6)*(7*n+3)*a(n-1)=0. - R. J. Mathar, Dec 22 2013
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=10.
MATHEMATICA
Table[10 Binomial[7 n + 10, n]/(7 n + 10), {n, 0, 40}] (* Vincenzo Librandi, Dec 23 2013 *)
PROG
(PARI) a(n) = 10*binomial(7*n+10, n)/(7*n+10);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/10))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [10*Binomial(7*n+10, n)/(7*n+10): n in [0..30]]; // Vincenzo Librandi, Dec 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 17 2013
STATUS
approved