A234527 2*binomial(10*n+4,n)/(5*n+2).

1, 4, 46, 704, 12341, 234260, 4685898, 97274544, 2075959314, 45262862788, 1003884090440, 22577660493024, 513698787408521, 11802947663348800, 273471432969603198, 6382396843322710560, 149902629054480517590, 3540479504783000035464

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=4.

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

Programs

Magma

[2*Binomial(10*n+4, n)/(5*n+2): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013

Mathematica

Table[2 Binomial[10 n + 4, n]/(5 n + 2), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)

PARI

a(n) = 2*binomial(10*n+4,n)/(5*n+2);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/2))^4+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=4.