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A229963 a(n) = 11*binomial(10*n + 11, n)/(10*n + 11) . 14
1, 11, 165, 2860, 53900, 1072797, 22188859, 472214600, 10273141395, 227440759700, 5107663394691, 116068178638776, 2664012608972000, 61668340817988135, 1438101958237201950, 33753007927148177360, 796704536753910327114 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r,n)/(n*p + r), where p = 10, r = 11.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906 [math.CO], 2007.

J-C. Aval, Multivariate Fuss-Catalan Numbers, 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.

Wikipedia, Fuss-Catalan number

FORMULA

G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 10, r = 11.

From _Peter Bala, Oct 16 2015: (Start)

O.g.f. A(x) = 1/x * series reversion (x*C(-x)^11), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. See cross-references for other Fuss-Catalan sequences with o.g.f. 1/x * series reversion (x*C(-x)^k), k = 3 through 11.

A(x)^(1/11) is the o.g.f. for A062744. (End)

MATHEMATICA

Table[11/(10 n + 11) Binomial[10 n + 11, n], {n, 0, 40}] (* Vincenzo Librandi, Jan 10 2014 *)

PROG

(PARI) a(n) = 11*binomial(10*n+11, n)/(10*n+11);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(10/11))^11+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [11*Binomial(10*n+11, n)/(10*n+11) : n in [0..20]]; // Vincenzo Librandi, Jan 10 2014

CROSSREFS

Cf. A000108, A062744, A234525, A234526, A234527, A234528, A234529, A234570, A234571, A234573.

Cf. A000245 (k = 3), A006629 (k = 4), A196678 (k = 5), A233668 (k = 6), A233743 (k = 7), A233835 (k = 8), A234467 (k = 9), A232265 (k = 10).

Sequence in context: A205086 A141876 A174364 * A051619 A261504 A142513

Adjacent sequences:  A229960 A229961 A229962 * A229964 A229965 A229966

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Oct 04 2013

EXTENSIONS

Corrected by Vincenzo Librandi, Jan 10 2014

STATUS

approved

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Last modified October 14 04:44 EDT 2019. Contains 327995 sequences. (Running on oeis4.)