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URL: https://oeis.org/A234869

⇱ A234869 - OEIS

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A234869
a(n) = 3*binomial(11*n+3,n)/(11*n+3).
9
1, 3, 36, 595, 11385, 237006, 5212064, 119126865, 2801765835, 67365151700, 1648369018296, 40914062713953, 1027625691201200, 26069631471224820, 667024542735629400, 17193066926119888716, 446028709678732029135, 11636873606948476550895, 305138071497541644423600
OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=3.
LINKS
Jean-Christophe Aval, Multivariate Fuss-Catalan Numbers, Discrete Math., Vol. 308, No. 20 (2008), 4660-4669; arXiv preprint, arXiv:0711.0906 [math.CO], 2007.
Thomas A. Dowling, Catalan Numbers, Chapter 7 of Applications of discrete mathematics, John G. Michaels and Kenneth H. Rosen (eds.), McGraw-Hill, New York, 1991. [Wayback Machine link]
Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15 (2010), 939-955.
FORMULA
G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, with p=11, r=3.
a(n) ~ 3 * 11^(11*n+5/2) / (4^(5*n+2) * 5^(10*n+7/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 13 2025
a(n) = A234870(n)*3*(5*n+2)/(2*(11*n+3)). - R. J. Mathar, Mar 18 2026
MATHEMATICA
Table[3 Binomial[11 n + 3, n]/(11 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Jan 01 2014 *)
PROG
(PARI) a(n) = 3*binomial(11*n+3, n)/(11*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/3))^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(11*n+3, n)/(11*n+3): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Fulford, Jan 01 2014
STATUS
approved