A234526 a(n) = 3*binomial(10*n+3,n)/(10*n+3).

1, 3, 33, 496, 8610, 162435, 3235501, 66959532, 1425658806, 31026962395, 687124547340, 15434728080408, 350818684083868, 8053515040969200, 186457795206547635, 4348790005989493960, 102080931442008205230, 2409777235191897422982, 57172751576200719537715, 1362539683633507445959200

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=3.

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.

Formula

G.f. satisfies: A(x) = (1 + x*A(x)^(p/r))^r, where p=10, r=3.

a(n) ~ 4^(5*n+1) * 5^(10*n+5/2) / (3^(18*n+6) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 14 2025

Mathematica

Table[3 Binomial[10 n + 3, n]/(10 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)

Prog

(PARI) a(n) = 3*binomial(10*n+3, n)/(10*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/3))^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(10*n+3, n)/(10*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013

Crossrefs

Cf. A000108, A059968, A234525, A234527, A234528, A234529, A234570, A234571, A234573, A229963.

Sequence in context: A368442 A264833 A071405 * A243251 A336539 A221147

Adjacent sequences: A234523 A234524 A234525 * A234527 A234528 A234529

Keyword

nonn

Author

Tim Fulford, Dec 27 2013

Status

approved