A233827 a(n) = 8*binomial(6*n+8,n)/(6*n+8).

1, 8, 76, 800, 8990, 105672, 1283464, 15981504, 202927725, 2617624680, 34206162848, 451872681728, 6024664312030, 80964348872400, 1095590286231120, 14915165412813184, 204140673966231870, 2807362363541687280, 38772186055550141700

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, 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.

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=6, r=8.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 5F5(4/3,3/2,5/3,11/6,13/6; 1,9/5,11/5,12/5,13/5; 46656*x/3125).

a(n) ~ 3^(6*n+15/2)*4^(3*n+5)/(sqrt(Pi)*5^(5*n+17/2)*n^(3/2)). (End)

Mathematica

Table[8 Binomial[6 n + 8, n]/(6 n + 8), {n, 0, 30}]

Prog

(PARI) a(n) = 8*binomial(6*n+8, n)/(6*n+8);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(6/8))^8+x*O(x^n)); polcoeff(B, n)}
(Magma) [8*Binomial(6*n+8, n)/(6*n+8): n in [0..30]];

Crossrefs

Cf. A000108, A002295, A212071, A212072, A212073, A130564, A233743, A233829, A233830.

Sequence in context: A083234 A247744 A144851 * A231286 A251927 A024281

Adjacent sequences: A233824 A233825 A233826 * A233828 A233829 A233830

Keyword

nonn

Author

Tim Fulford, Dec 16 2013

Status

approved