A234525 Binomial(10*n+2,n)/(5*n+1).

1, 2, 21, 310, 5330, 99960, 1983049, 40919714, 869304150, 18885977110, 417663940540, 9371084905962, 212791660837756, 4880918206648000, 112925143575796455, 2632162372046272660, 61752662230350642670, 1457074607325333325524

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=2.

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, A234526, A234527, A234528, A234529, A234570, A234571, A234573, A229963.

Programs

Magma

[Binomial(10*n+2, n)/(5*n+1): n in [0..30]]; // Vincenzo Librandi, Dec 27 2013

Mathematica

Table[Binomial[10 n + 2, n]/(5 n + 1), {n, 0, 40}] (* Vincenzo Librandi, Dec 27 2013 *)

PARI

a(n) = binomial(10*n+2,n)/(5*n+1);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^5)^2+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=2.

a(n) = 2*binomial(10n+1,n-1)/n for n>0, a(0)=1. [Bruno Berselli, Jan 19 2014]