A234872 a(n) = 6*binomial(11*n+6,n)/(11*n+6).

1, 6, 81, 1406, 27636, 585162, 13019909, 300138696, 7105216833, 171717015470, 4219267597578, 105085831400550, 2647012241261856, 67316157557021436, 1726006087183713615, 44570883175043934384, 1158139943222389790715

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=6.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

J-C. 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.

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, with p=11, r=6.

a(n) ~ 3*4^(-3-5*n)*5^(-13/2-10*n)*11^(11/2+11*n)/(n^(3/2)*sqrt(Pi)). - Stefano Spezia, Aug 23 2025

D-finite with recurrence 800*n *(10*n+1) *(5*n+1) *(10*n+3) *(5*n+2) *(2*n+1) *(5*n+3) *(10*n-3) *(5*n-1) *(10*n-1) *a(n) -11*(11*n-5) *(11*n+1) *(11*n-4) *(11*n+2) *(11*n-3) *(11*n+3) *(11*n-2) *(11*n+4) *(11*n-1) *(11*n+5)*a(n-1)=0. - R. J. Mathar, Mar 18 2026

Mathematica

Table[6 Binomial[11 n + 6, n]/(11 n + 6), {n, 0, 40}] (* Vincenzo Librandi, Jan 01 2014 *)

Prog

(PARI) a(n) = 6*binomial(11*n+6, n)/(11*n+6);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/6))^6+x*O(x^n)); polcoeff(B, n)}
(Magma) [6*Binomial(11*n+6, n)/(11*n+6): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Crossrefs

Cf. A230388, A234868, A234869, A234870, A234871, A234873.

Sequence in context: A373939 A377262 A377267 * A064341 A372321 A349505

Adjacent sequences: A234869 A234870 A234871 * A234873 A234874 A234875

Keyword

nonn

Author

Tim Fulford, Jan 01 2014

Status

approved