A233908 a(n) = 10*binomial(7*n+10,n)/(7*n+10).

1, 10, 115, 1450, 19425, 271502, 3915100, 57821940, 870238200, 13298907050, 205811513765, 3218995093860, 50802419972395, 808016193159000, 12938696992921000, 208419656266988904, 3374960506795660365, 54907659530154222000, 897060906625956765000, 14711500799506081410000

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=10.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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. Math. 15 (2010), 939-955.

Wikipedia, Fuss-Catalan number.

Formula

G.f. satisfies: A(x) = (1 + x*A(x)^(p/r))^r, where p=7, r=10.

72*n*(6*n+5)*(3*n+5)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) - 7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+9)*(7*n+6)*(7*n+3)*a(n-1) = 0. - R. J. Mathar, Dec 22 2013

a(n) ~ 5 * 7^(7*n+19/2) / (3^(6*n+21/2) * 4^(3*n+5) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 15 2025

Mathematica

Table[10 Binomial[7 n + 10, n]/(7 n + 10), {n, 0, 40}] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(PARI) a(n) = 10*binomial(7*n+10, n)/(7*n+10);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/10))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [10*Binomial(7*n+10, n)/(7*n+10): n in [0..30]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A000108, A002296, A233832, A233833, A233834, A233835, A143547, A130565, A233907.

Sequence in context: A104520 A138845 A079678 * A089833 A308667 A384593

Adjacent sequences: A233905 A233906 A233907 * A233909 A233910 A233911

Keyword

nonn

Author

Tim Fulford, Dec 17 2013

Status

approved