A233667 a(n) = 5*binomial(4*n+10,n)/(2*n+5).

1, 10, 85, 700, 5750, 47502, 395560, 3321120, 28102425, 239503550, 2054455634, 17726454200, 153757722300, 1340045361750, 11729338225200, 103068670351552, 908923976461140, 8041606944709800, 71359997110169625, 634978885837495500, 5664526697522326590

Offset: 0

Author

Tim Fulford, Dec 14 2013

Keywords

• nonn
• easy

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=4, 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, A002293, A069271, A006632, A196678, A006633, A233658, A233666, A006634, A006635.

Programs

Magma

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

Mathematica

Table[5 Binomial[4 n + 10, n]/(2 n + 5), {n, 0, 30}]

PARI

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

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/5))^10+x*O(x^n)); polcoeff(B, n)}

Formula

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

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 4F4(5/2,11/4,3,13/4; 1,11/3,4,13/3; 256*x/27).

a(n) ~ 5*2^(8*n+39/2)/(sqrt(Pi)*3^(3*n+21/2)*n^(3/2)). (End)