login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233832 a(n) = 2*binomial(7*n+2,n)/(7*n+2). 6
1, 2, 15, 154, 1827, 23562, 320866, 4540200, 66096459, 983592304, 14894775896, 228784720710, 3555866673450, 55819631671902, 883738853546472, 14094715154157680, 226245021605612955, 3652242142988400570, 59254515909624764575, 965678197027521177200 (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=7, r=2.

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.

Wikipedia, Fuss-Catalan number

FORMULA

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=2.

a(n) = 2*binomial(7n+1, n-1)/n for n>0, a(0)=1. [Bruno Berselli, Jan 19 2014]

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 6F6(2/7,3/7,4/7,5/7,6/7,8/7; 1/2,2/3,5/6,1,7/6,4/3; 823543*x/46656).

a(n) ~ 7^(7*n+3/2)/(sqrt(Pi)*3^(6*n+5/2)*4^(3*n+1)*n^(3/2)). (End)

MATHEMATICA

Table[2 Binomial[7 n + 2, n]/(7 n + 2), {n, 0, 30}]

PROG

(PARI) a(n) = 2*binomial(7*n+2, n)/(7*n+2);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/2))^2+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [2*Binomial(7*n+2, n)/(7*n+2): n in [0..30]];

CROSSREFS

Cf. A000108, A002296, A233833 - A233835, A143547, A130565, A233907, A233908.

Sequence in context: A002103 A191364 A308379 * A185756 A239107 A124548

Adjacent sequences:  A233829 A233830 A233831 * A233833 A233834 A233835

KEYWORD

nonn

AUTHOR

Tim Fulford, Dec 16 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 November 15 18:29 EST 2019. Contains 329149 sequences. (Running on oeis4.)