A234509 2*binomial(9*n+6,n)/(3*n+2).

1, 6, 69, 992, 15990, 276360, 5006386, 93817152, 1803606255, 35373572460, 704995403541, 14236901646240, 290687378847684, 5990903682047592, 124463414269524000, 2603845580096662656, 54807372993836345589, 1159856934027109448130, 24663454505518980363102, 526708243449729452311200, 11291926596343014148087470

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=6.

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=9, r=6.

Mathematica

Table[6 Binomial[9 n + 6, n]/(9 n + 6), {n, 0, 30}]

Prog

(PARI) a(n) = 2*binomial(9*n+6, n)/(3*n+2);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/2))^6+x*O(x^n)); polcoeff(B, n)}
(Magma) [2*Binomial(9*n+6, n)/(3*n+2): n in [0..30]];

Crossrefs

Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234510, A234513, A232265.

Sequence in context: A258792 A214694 A347674 * A177751 A338176 A235327

Adjacent sequences: A234506 A234507 A234508 * A234510 A234511 A234512

Keyword

nonn

Author

Tim Fulford, Dec 27 2013

Status

approved