A233908 10*binomial(7*n+10,n)/(7*n+10).

1, 10, 115, 1450, 19425, 271502, 3915100, 57821940, 870238200, 13298907050, 205811513765, 3218995093860, 50802419972395, 808016193159000, 12938696992921000, 208419656266988904, 3374960506795660365, 54907659530154222000, 897060906625956765000

Offset: 0

Author

Tim Fulford, Dec 17 2013

Keywords

• nonn

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=7, 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.
• Wikipedia, Fuss-Catalan number

Crossrefs

Cf. A000108, A002296, A233832 - A233835, A143547, A130565, A233907.

Programs

Magma

[10*Binomial(7*n+10, n)/(7*n+10): n in [0..30]]; // Vincenzo Librandi, Dec 23 2013

Mathematica

Table[10 Binomial[7 n + 10, n]/(7 n + 10), {n, 0, 40}] (* Vincenzo Librandi, Dec 23 2013 *)

PARI

a(n) = 10*binomial(7*n+10,n)/(7*n+10);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/10))^10+x*O(x^n)); polcoeff(B, n)}

Formula

72*n*(6*n+5)*(3*n+5)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) -7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+9)*(7*n+6)*(7*n+3)*a(n-1)=0. - R. J. Mathar, Dec 22 2013

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=10.