A235338 a(n) = 8*binomial(11*n+8,n)/(11*n+8).

1, 8, 116, 2080, 41650, 892552, 20027112, 464550336, 11050084695, 268070745800, 6607118937848, 164979021222400, 4164615224071926, 106105019316578800, 2724883054841727200, 70462458864489354624, 1833143662625459289495

Offset: 0

Author

Tim Fulford, Jan 06 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=8.

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 [broken link]
• Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955.

Crossrefs

Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235339, A235340.

Programs

Magma

[8*Binomial(11*n+8, n)/(11*n+8): n in [0..30]];

Mathematica

Table[8 Binomial[11 n + 8, n]/(11 n + 8), {n, 0, 30}]

PARI

a(n) = 8*binomial(11*n+8, n)/(11*n+8);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/8))^8+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p=11, r=8.