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

0,2

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

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, 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

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

Sequence in context: A280358 A114480 A123356 * A139087 A349655 A173218

Adjacent sequences: A234867 A234868 A234869 * A234871 A234872 A234873

Keyword

nonn

Author

Tim Fulford, Jan 01 2014

Status

approved