A234508 5*binomial(9*n+5,n)/(9*n+5).

1, 5, 55, 775, 12350, 211876, 3818430, 71282640, 1366368375, 26735839650, 531838637759, 10723307329700, 218658647805780, 4501362056183300, 93426735902060000, 1952884185072496992, 41074876852203972645, 868669222741822476975, 18460669540059117038250, 394033629095915025876750, 8443512680148379948569910

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=9, 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, A143554, A234505, A234506, A234507, A234509, A234510, A234513, A232265.

Programs

Magma

[5*Binomial(9*n+5, n)/(9*n+5): n in [0..30]];

Mathematica

Table[5 Binomial[9 n + 5, n]/(9 n + 5), {n, 0, 30}]

PARI

a(n) = 5*binomial(9*n+5,n)/(9*n+5);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/5))^5+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=5.