A233907 9*binomial(7*n+9, n)/(7*n+9).

1, 9, 99, 1218, 16065, 222138, 3178140, 46656324, 698868216, 10639125640, 164128169205, 2560224004884, 40314178429707, 639948824981928, 10230035192533800, 164541833894991240, 2660919275605834701, 43239781879996449825, 705687913212419321800, 11561996402992103418000, 190100812111989146008641

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=9.

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, A002296, A233832, A233833, A143547, A233834, A130565, A233835, A233908.

Programs

Magma

[9*Binomial(7*n+9, n)/(7*n+9): n in [0..30]];

Mathematica

Table[9 Binomial[7 n + 9, n]/(7 n + 9), {n, 0, 30}]

PARI

a(n) = 9*binomial(7*n+9,n)/(7*n+9);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/9))^9+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=9.

D-finite with recurrence 72*n*(6*n+5)*(3*n+2)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) -7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+2)*(7*n+6)*(7*n+3)*a(n-1)=0. - R. J. Mathar, Nov 22 2024