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A234525
Binomial(10*n+2,n)/(5*n+1).
11
1, 2, 21, 310, 5330, 99960, 1983049, 40919714, 869304150, 18885977110, 417663940540, 9371084905962, 212791660837756, 4880918206648000, 112925143575796455, 2632162372046272660, 61752662230350642670, 1457074607325333325524
OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=2.
LINKS
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=2.
a(n) = 2*binomial(10n+1,n-1)/n for n>0, a(0)=1. [Bruno Berselli, Jan 19 2014]
MATHEMATICA
Table[Binomial[10 n + 2, n]/(5 n + 1), {n, 0, 40}] (* Vincenzo Librandi, Dec 27 2013 *)
PROG
(PARI) a(n) = binomial(10*n+2, n)/(5*n+1);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^5)^2+x*O(x^n)); polcoeff(B, n)}
(Magma) [Binomial(10*n+2, n)/(5*n+1): n in [0..30]]; // Vincenzo Librandi, Dec 27 2013
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 27 2013
STATUS
approved