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A234506 Binomial(9*n+3)/(3*n+1). 8
1, 3, 30, 406, 6327, 107019, 1909908, 35399520, 674842149, 13147742322, 260626484118, 5239783981320, 106585537781775, 2189670831627678, 45366284782209600, 946815917066740800, 19887218367823853937, 420076689292591271325, 8917736795123409615060, 190161017612160607167948, 4071301730663135449185705 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=3.

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=3.

MATHEMATICA

Table[ Binomial[9 n + 3, n]/(3 n + 1), {n, 0, 30}]

PROG

(PARI) a(n) = binomial(9*n+3, n)/(3*n+1);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^3)^3+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [Binomial(9*n+3, n)/(3*n+1): n in [0..30]];

CROSSREFS

Cf. A000108, A143554, A234505, A234507, A234508, A234509, A234510, A234513, A232265.

Sequence in context: A229299 A178016 A058831 * A212425 A294240 A007004

Adjacent sequences:  A234503 A234504 A234505 * A234507 A234508 A234509

KEYWORD

nonn

AUTHOR

Tim Fulford, Dec 27 2013

STATUS

approved

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Last modified May 20 20:16 EDT 2019. Contains 323426 sequences. (Running on oeis4.)