A234869 3*binomial(11*n+3,n)/(11*n+3).

1, 3, 36, 595, 11385, 237006, 5212064, 119126865, 2801765835, 67365151700, 1648369018296, 40914062713953, 1027625691201200, 26069631471224820, 667024542735629400, 17193066926119888716, 446028709678732029135, 11636873606948476550895

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=11, r=3.

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, with p=11, r=3.

Mathematica

Table[3 Binomial[11 n + 3, n]/(11 n + 3), {n, 0, 30}] (* Vincenzo Librandi, Jan 01 2014 *)

Prog

(PARI) a(n) = 3*binomial(11*n+3, n)/(11*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/3))^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(11*n+3, n)/(11*n+3): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

Crossrefs

Cf. A230388, A234868, A234870, A234871, A234872, A234873.

Sequence in context: A245114 A276018 A291096 * A371660 A305991 A203493

Adjacent sequences: A234866 A234867 A234868 * A234870 A234871 A234872

Keyword

nonn

Author

Tim Fulford, Jan 01 2014

Status

approved