A234529 3*binomial(10*n+6,n)/(5*n+3).

1, 6, 75, 1190, 21285, 409266, 8259888, 172593900, 3701885490, 81033954430, 1803028662435, 40658396849388, 927146157991625, 21342995124948000, 495322997953271580, 11576581508367256920, 272239271289546497046, 6437043284012559773100

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=6.

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, A234526, A234527, A234528, A234570, A234571, A234573, A229963.

Programs

Magma

[3*Binomial(10*n+6, n)/(5*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 27 2013

Mathematica

Table[3 Binomial[10 n + 6, n]/(5 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Dec 27 2013 *)

PARI

a(n) = 3*binomial(10*n+6,n)/(5*n+3);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/3))^6+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=6.