A233829 a(n) = 3*binomial(6*n+9,n)/(2*n+3).

1, 9, 90, 975, 11160, 132867, 1629012, 20430900, 260907075, 3381098545, 44352058608, 587787511779, 7858257798300, 105855415586550, 1435361957277480, 19576154604317304, 268364706225271110, 3695862686045572350, 51108790709588823150

Offset: 0

Author

Tim Fulford, Dec 16 2013

Keywords

• nonn

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, 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, A002295, A212071, A212072, A212073, A130564, A233743, A233827, A233830.

Programs

Magma

[3*Binomial(6*n+9, n)/(2*n+3): n in [0..30]];

Mathematica

Table[3 Binomial[6 n + 9, n]/(2 n + 3), {n, 0, 30}]

PARI

a(n) = 3*binomial(6*n+9,n)/(2*n+3);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/3))^9+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=6, r=9.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 5F5(3/2,5/3,11/6,13/6,7/3; 1,11/5,12/5,13/5,14/5; 46656*x/3125).

a(n) ~ 3^(6*n+21/2)*4^(3*n+4)/(sqrt(Pi)*5^(5*n+19/2)*n^(3/2)). (End)