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A234526
3*binomial(10*n+3,n)/(10*n+3).
9
1, 3, 33, 496, 8610, 162435, 3235501, 66959532, 1425658806, 31026962395, 687124547340, 15434728080408, 350818684083868, 8053515040969200, 186457795206547635, 4348790005989493960, 102080931442008205230, 2409777235191897422982
OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=3.
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=10, r=3.
MATHEMATICA
Table[3 Binomial[10 n + 3, n]/(10 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)
PROG
(PARI) a(n) = 3*binomial(10*n+3, n)/(10*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/3))^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(10*n+3, n)/(10*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 27 2013
STATUS
approved