A234870 4*binomial(11*n+4,n)/(11*n+4).

1, 4, 50, 840, 16215, 339416, 7492342, 171714400, 4046995095, 97464474800, 2388021782916, 59337354111464, 1491714713034000, 37872300445759440, 969656048236053850, 25008097347083474496, 649098691321081570855, 16942574600154870074100

Offset: 0

Author

Tim Fulford, Jan 01 2014

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A230388, A234868, A234869, A234871, A234872, A234873.

Programs

Magma

[4*Binomial(11*n+4,n)/(11*n+4): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Mathematica

Table[4 Binomial[11 n + 4, n]/(11 n + 4), {n, 0, 40}] (* Vincenzo Librandi, Jan 01 2014 *)

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)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, with p=11, r=4.