A234528 Binomial(10*n+5,n)/(2*n+1).

1, 5, 60, 935, 16555, 316251, 6353760, 132321990, 2830853610, 61841702065, 1373736123760, 30935736733230, 704631080073635, 16204866668942000, 375762274309378440, 8775795659568727020, 206241872189050376550, 4873761343609509542490

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=5.

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, A234529, A234570, A234571, A234573, A229963.

Programs

Magma

[Binomial(10*n+5, n)/(2*n+1): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013

Mathematica

Table[Binomial[10 n + 5, n]/(2 n + 1), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)

PARI

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

PARI

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

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=5.