A234868 a(n) = 2*binomial(11*n+2,n)/(11*n+2).

1, 2, 23, 374, 7095, 146916, 3219216, 73386170, 1722567143, 41352865400, 1010607195741, 25058477434562, 628845572227600, 15941429819185752, 407626109449551300, 10501154649486399096, 272294680440574235015, 7101160966497659412010, 186134223613500403098396

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=2; also, g.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Jean-Christophe Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906 [math.CO], 2007; 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, A234869, A234870, A234871, A234872, A234873.

Programs

Magma

[2*Binomial(11*n+2,n)/(11*n+2): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Mathematica

Table[2 Binomial[11 n + 2, n]/(11 n + 2), {n, 0, 30}] (* Vincenzo Librandi, Jan 01 2014 *)

PARI

a(n) = 2*binomial(11*n+2,n)/(11*n+2)
for(n=0,20, print(a(n))) \\ Sequence

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/2))^2+x*O(x^n)); polcoeff(B, n)}
for (n=0,20, print(a(n))) \\ Generating Function

Sage

[2*binomial(11*n+2,n)/(11*n+2) for n in range(20)] # F. Chapoton; Apr 29 2020

Formula

a(n) = 2*binomial(11*n+1,n-1)/n for n>0, a(0)=1. [Bruno Berselli, Jan 19 2014]