A229963 a(n) = 11*binomial(10*n + 11, n)/(10*n + 11) .
1, 11, 165, 2860, 53900, 1072797, 22188859, 472214600, 10273141395, 227440759700, 5107663394691, 116068178638776, 2664012608972000, 61668340817988135, 1438101958237201950, 33753007927148177360, 796704536753910327114
Offset: 0
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
Crossrefs
Programs
-
Magma
[11*Binomial(10*n+11,n)/(10*n+11) : n in [0..20]]; // Vincenzo Librandi, Jan 10 2014
-
Mathematica
Table[11/(10 n + 11) Binomial[10 n + 11, n], {n, 0, 40}] (* Vincenzo Librandi, Jan 10 2014 *) -
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)}
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 A059968. (End)
D-finite with recurrence: 81*n*(9*n+11)*(9*n+4)*(3*n+2)*(9*n+8)*(9*n+10)*(3*n+1)*(9*n+5)*(9*n+7)*a(n) -800*(10*n+1)*(5*n+1)*(10*n+3)*(5*n+2)*(2*n+1)*(5*n+3)*(10*n+7)*(5*n+4)*(10*n+9)*a(n-1)=0. - R. J. Mathar, Feb 21 2020
Extensions
Corrected by Vincenzo Librandi, Jan 10 2014
Comments