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A234467 a(n) = 9*binomial(8*n + 9,n)/(8*n + 9). 15
1, 9, 108, 1488, 22230, 350244, 5729724, 96395616, 1657248417, 28987537150, 514215324216, 9229030737264, 167283594343320, 3057857090083908, 56305821384711720, 1043424549990820800, 19445145508444588200, 364191559218548917713, 6851518654436447733980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r,n)/(n*p + r); this is the case p = 8, r = 9.

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.

J-C. Aval, Multivariate Fuss-Catalan Numbers, 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.

Wikipedia, Fuss-Catalan number

FORMULA

G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 8, r = 9.

From _Peter Bala, Oct 16 2015: (Start)

O.g.f. A(x) = 1/x * series reversion (x*C(-x)^9), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. See cross-references for other Fuss-Catalan sequences with o.g.f. 1/x * series reversion (x*C(-x)^k), k = 3 through 11.

A(x)^(1/9) is the o.g.f. for A007556. (End)

MATHEMATICA

Table[9 Binomial[8 n + 9, n]/(8 n + 9), {n, 0, 40}] (* Vincenzo Librandi, Dec 26 2013 *)

PROG

(PARI) a(n) = 9*binomial(8*n+9, n)/(8*n+9);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(8/9))^9+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [9*Binomial(8*n+9, n)/(8*n+9): n in [0..30]]; // Vincenzo Librandi, Dec 26 2013

CROSSREFS

Cf. A007556, A234461, A234462, A234463, A234464, A234465, A234466.

Cf. A000108, A000245 (k = 3), A006629 (k = 4), A196678 (k = 5), A233668 (k = 6), A233743 (k = 7), A233835 (k = 8),  A232265 (k = 10), A229963 (k = 11).

Sequence in context: A099676 A268839 A214668 * A288550 A166907 A051606

Adjacent sequences:  A234464 A234465 A234466 * A234468 A234469 A234470

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Dec 26 2013

STATUS

approved

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)