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A234872 6*binomial(11*n+6,n)/(11*n+6). 9
1, 6, 81, 1406, 27636, 585162, 13019909, 300138696, 7105216833, 171717015470, 4219267597578, 105085831400550, 2647012241261856, 67316157557021436, 1726006087183713615, 44570883175043934384, 1158139943222389790715 (list; graph; refs; listen; history; text; internal format)
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=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, with p=11, r=6.

MATHEMATICA

Table[6 Binomial[11 n + 6, n]/(11 n + 6), {n, 0, 40}] (* Vincenzo Librandi, Jan 01 2014 *)

PROG

(PARI) a(n) = 6*binomial(11*n+6, n)/(11*n+6);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/6))^6+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [6*Binomial(11*n+6, n)/(11*n+6): n in [0..30]]; // Vincenzo Librandi, Jan 01 2014

CROSSREFS

Cf. A230388, A234868, A234869, A234870, A234871, A234873.

Sequence in context: A309902 A196909 A197076 * A064341 A349505 A052756

Adjacent sequences:  A234869 A234870 A234871 * A234873 A234874 A234875

KEYWORD

nonn

AUTHOR

Tim Fulford, Jan 01 2014

STATUS

approved

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Last modified December 8 19:45 EST 2021. Contains 349596 sequences. (Running on oeis4.)