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A234870
4*binomial(11*n+4,n)/(11*n+4).
9
1, 4, 50, 840, 16215, 339416, 7492342, 171714400, 4046995095, 97464474800, 2388021782916, 59337354111464, 1491714713034000, 37872300445759440, 969656048236053850, 25008097347083474496, 649098691321081570855, 16942574600154870074100
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=4.
LINKS
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, with p=11, r=4.
MATHEMATICA
Table[4 Binomial[11 n + 4, n]/(11 n + 4), {n, 0, 40}] (* Vincenzo Librandi, Jan 01 2014 *)
PROG
(PARI) a(n) = 4*binomial(11*n+4, n)/(11*n+4);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/4))^4+x*O(x^n)); polcoeff(B, n)}
(Magma) [4*Binomial(11*n+4, n)/(11*n+4): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Jan 01 2014
STATUS
approved