A234526 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

Offset: 0

Author

Tim Fulford, Dec 27 2013

Keywords

• nonn

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
• 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.

Crossrefs

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

Programs

Magma

[3*Binomial(10*n+3, n)/(10*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013

Mathematica

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

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)}

Formula

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