A233736 a(n) = 8*binomial(5*n + 8, n)/(5*n + 8).

1, 8, 68, 616, 5850, 57536, 581196, 5995184, 62891499, 668922800, 7197169980, 78195588168, 856708896784, 9454328800896, 104997940138300, 1172624772468960, 13161188646791865, 148375147999406328, 1679436658449372744, 19078164706488179600

Offset: 0

Author

Tim Fulford, Dec 15 2013

Keywords

• nonn

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=5, r=8.

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. A000108, A002294, A118969, A143546, A118971, A233668, A233669, A233737, A233738.

Programs

Magma

[8*Binomial(5*n+8,n)/(5*n+8): n in [0..30]]; // Vincenzo Librandi, Dec 16 2013

Mathematica

Table[8 Binomial[5 n + 8, n]/(5 n + 8), {n, 0, 40}] (* Vincenzo Librandi, Dec 16 2013 *)

PARI

a(n) = 8*binomial(5*n+8,n)/(5*n+8);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/8))^8+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=5, r=8.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 5F5(8/5,9/5,2,11/5,12/5; 1,9/4,5/2,11/4,3; 3125*x/256).

a(n) ~ 5^(5*n+15/2)/(sqrt(Pi)*2^(8*n+29/2)*n^(3/2)). (End)