A234871 a(n) = 5*binomial(11*n+5,n)/(11*n+5).

1, 5, 65, 1110, 21620, 455126, 10085845, 231814440, 5475346305, 132090011900, 3240886705386, 80621405042750, 2028732009726240, 51548408940061460, 1320738410528418175, 34083616545621832176, 885134579074202142075, 23114512490211287029665

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=5.

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, A234870, A234872, A234873.

Programs

Magma

[5*Binomial(11*n+5,n)/(11*n+5): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Mathematica

Table[5 Binomial[11 n + 5, n]/(11 n + 5), {n, 0, 40}] (* Vincenzo Librandi, Jan 01 2014 *)

PARI

a(n) = 5*binomial(11*n+5,n)/(11*n+5);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/5))^5+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, with p=11, r=5.