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!)
A233736 a(n) = 8*binomial(5*n + 8, n)/(5*n + 8). 5
1, 8, 68, 616, 5850, 57536, 581196, 5995184, 62891499, 668922800, 7197169980, 78195588168, 856708896784, 9454328800896, 104997940138300, 1172624772468960, 13161188646791865, 148375147999406328, 1679436658449372744, 19078164706488179600 (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=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=5, r=8.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 5F5(8/5,9/5,2,11/5,12/5; 1,9/4,5/2,11/4,3; 3125*x/256).

a(n) ~ 5^(5*n+15/2)/(sqrt(Pi)*2^(8*n+29/2)*n^(3/2)). (End)

MATHEMATICA

Table[8 Binomial[5 n + 8, n]/(5 n + 8), {n, 0, 40}] (* Vincenzo Librandi, Dec 16 2013 *)

PROG

(PARI) a(n) = 8*binomial(5*n+8, n)/(5*n+8);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/8))^8+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [8*Binomial(5*n+8, n)/(5*n+8): n in [0..30]]; // Vincenzo Librandi, Dec 16 2013

CROSSREFS

Cf. A000108, A002294, A118969, A143546, A118971, A233668, A233669, A233737, A233738.

Sequence in context: A281337 A152105 A068766 * A279266 A054915 A073555

Adjacent sequences:  A233733 A233734 A233735 * A233737 A233738 A233739

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 June 1 07:40 EDT 2020. Contains 334759 sequences. (Running on oeis4.)