A234873 a(n) = 7*binomial(11*n+7,n)/(11*n+7).

1, 7, 98, 1729, 34300, 730597, 16323468, 377447148, 8956384437, 216859117475, 5336519142108, 133078780790725, 3355661187741408, 85414540549845934, 2191753761503128400, 56636249639625891144, 1472525237190942707955, 38493320646256331312268, 1011120027044157531213720

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=7.

Links

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

Jean-Christophe Aval, Multivariate Fuss-Catalan Numbers, Discrete Math., Vol. 308, No. 20 (2008), 4660-4669; arXiv preprint, arXiv:0711.0906 [math.CO], 2007.

Thomas A. Dowling, Catalan Numbers, Chapter 7 of Applications of discrete mathematics, John G. Michaels and Kenneth H. Rosen (eds.), McGraw-Hill, New York, 1991. [Wayback Machine link]

Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15 (2010), 939-955.

Formula

G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, with p=11, r=7.

a(n) ~ 7 * 11^(11*n+13/2) / (4^(5*n+4) * 5^(10*n+15/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 13 2025

Mathematica

Table[7 Binomial[11 n + 7, n]/(11 n + 7), {n, 0, 30}] (* Vincenzo Librandi, Jan 01 2014 *)

Prog

(PARI) a(n) = 7*binomial(11*n+7, n)/(11*n+7);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/7))^7+x*O(x^n)); polcoeff(B, n)}
(Magma) [7*Binomial(11*n+7, n)/(11*n+7): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Crossrefs

Cf. A230388, A234868, A234869, A234870, A234871, A234872.

Sequence in context: A237022 A385206 A156266 * A051188 A367138 A113134

Adjacent sequences: A234870 A234871 A234872 * A234874 A234875 A234876

Keyword

nonn

Author

Tim Fulford, Jan 01 2014

Status

approved