login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233737 a(n) = 9*binomial(5*n+9, n)/(5*n+9). 5
1, 9, 81, 759, 7371, 73656, 752913, 7838298, 82832706, 886322710, 9583986555, 104568156819, 1149793519368, 12728471356944, 141747219186705, 1586867219265060, 17848735288114995, 201607141031660871, 2285899896222757346, 26008027474874327190, 296840444852078282610, 3397721117411729991960 (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), this is the case p=5, r=9.

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, here p=5, r=9.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 5F5(9/5,2,11/5,12/5,13/5; 1,5/2,11/4,3,13/4; 3125*x/256).

a(n) ~ 9*5^(5*n+17/2)/(sqrt(Pi)*2^(8*n+39/2)*n^(3/2)). (End)

MATHEMATICA

Table[9 Binomial[5 n + 9, n]/(5 n + 9), {n, 0, 30}]

PROG

(PARI) a(n) = 9*binomial(5*n+9, n)/(5*n+9);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/9))^9+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [9*Binomial(5*n+9, n)/(5*n+9): n in [0..30]];

CROSSREFS

Cf. A000108, A002294, A118969, A143546, A118971, A233668, A233669, A233736, A233738.

Sequence in context: A033145 A158762 A101601 * A344298 A144821 A344253

Adjacent sequences:  A233734 A233735 A233736 * A233738 A233739 A233740

KEYWORD

nonn

AUTHOR

Tim Fulford, Dec 15 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 16:31 EDT 2021. Contains 346359 sequences. (Running on oeis4.)