OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=4, r=7.
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.
FORMULA
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=4, r=7.
D-finite with recurrence 3*(3*n+5)*(3*n+7)*(n+2)*a(n) -(n+1)*(661*n^2+1301*n+558)*a(n-1) +120*(4*n+1)*(2*n+1)*(4*n-1)*a(n-2)=0. - R. J. Mathar, Nov 22 2024
D-finite with recurrence 3*n*(3*n+5)*(3*n+7)*(n+2)*a(n) -8*(4*n+5)*(2*n+3)*(4*n+3)*(n+1)*a(n-1)=0. - R. J. Mathar, Nov 22 2024
MATHEMATICA
Table[7 Binomial[4 n + 7, n]/(4 n + 7), {n, 0, 30}]
PROG
(PARI) a(n) = 7*binomial(4*n+7, n)/(4*n+7);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/7))^7+x*O(x^n)); polcoeff(B, n)}
(Magma) [7*Binomial(4*n+7, n)/(4*n+7): n in [0..30]];
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Tim Fulford, Dec 14 2013
STATUS
approved