A234529 3*binomial(10*n+6,n)/(5*n+3).

1, 6, 75, 1190, 21285, 409266, 8259888, 172593900, 3701885490, 81033954430, 1803028662435, 40658396849388, 927146157991625, 21342995124948000, 495322997953271580, 11576581508367256920, 272239271289546497046, 6437043284012559773100

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=6.

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.

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=10, r=6.

Mathematica

Table[3 Binomial[10 n + 6, n]/(5 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Dec 27 2013 *)

Prog

(PARI) a(n) = 3*binomial(10*n+6, n)/(5*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/3))^6+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(10*n+6, n)/(5*n+3): n in [0..30]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A000108, A059968, A234525, A234526, A234527, A234528, A234570, A234571, A234573, A229963.

Sequence in context: A281797 A049235 A129031 * A139088 A193784 A162863

Adjacent sequences: A234526 A234527 A234528 * A234530 A234531 A234532

Keyword

nonn

Author

Tim Fulford, Dec 27 2013

Status

approved