A234873 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

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=7.

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, A234871, A234872.

Programs

Magma

[7*Binomial(11*n+7,n)/(11*n+7): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Mathematica

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

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)}

Formula

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