A230390 5*binomial(8*n+10,n)/(4*n+5).

1, 10, 125, 1760, 26650, 423752, 6978510, 117998400, 2036685765, 35738059500, 635627275767, 11433154297760, 207621482341000, 3801296492623560, 70092637731997100, 1300500163756675200, 24262157874835233000, 454847339247972377850, 8564398318045559667475

Offset: 0

Author

Tim Fulford, Dec 28 2013

Keywords

• nonn

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=8, r=10.

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, A007556, A234461, A234462, A234463, A234464, A234465, A234466, A234467.

Programs

Magma

[5*Binomial(8*n+10, n)/(4*n+5): n in [0..30]];

Mathematica

Table[5 Binomial[8 n + 10, n]/(4 n + 5), {n, 0, 30}]

PARI

a(n) = 5*binomial(8*n+10,n)/(4*n+5);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/5))^10+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=8, r=10.