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A233829
a(n) = 3*binomial(6*n+9,n)/(2*n+3).
4
1, 9, 90, 975, 11160, 132867, 1629012, 20430900, 260907075, 3381098545, 44352058608, 587787511779, 7858257798300, 105855415586550, 1435361957277480, 19576154604317304, 268364706225271110, 3695862686045572350, 51108790709588823150
OFFSET
0,2
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
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.
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)
MATHEMATICA
Table[3 Binomial[6 n + 9, n]/(2 n + 3), {n, 0, 30}]
PROG
(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)}
(Magma) [3*Binomial(6*n+9, n)/(2*n+3): n in [0..30]];
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 16 2013
STATUS
approved