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 A233738 2*binomial(5*n+10, n)/(n+2). 6
 1, 10, 95, 920, 9135, 92752, 959595, 10084360, 107375730, 1156073100, 12565671261, 137702922560, 1519842008360, 16880051620320, 188519028884675, 2115822959020080, 23851913523156675, 269958280013904870, 3066451080298820830, 34946186787944832400 (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=5, r=10. 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. FORMULA G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=5, r=10. a(n) = 2*A004344(n)/(n+2). - Wesley Ivan Hurt, Sep 07 2014 G.f.: hypergeom([2, 11/5, 12/5, 13/5, 14/5], [11/4, 3, 13/4, 7/2], (3125/256)*x). - Robert Israel, Sep 07 2014 MAPLE A233738:=n->2*binomial(5*n+10, n)/(n+2): seq(A233738(n), n=0..30); # Wesley Ivan Hurt, Sep 07 2014 MATHEMATICA Table[2 Binomial[5 n + 10, n]/(n + 2), {n, 0, 40}] (* Vincenzo Librandi, Dec 16 2013 *) PROG (PARI) a(n) = 2*binomial(5*n+10, n)/(n+2); (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(1/2))^10+x*O(x^n)); polcoeff(B, n)} (Magma) [2*Binomial(5*n+10, n)/(n+2): n in [0..30]]; // Vincenzo Librandi, Dec 16 2013 CROSSREFS Cf. A000108, A002294, A004344, A118969, A118971, A143546, A233668, A233669, A233736, A233737. Sequence in context: A259289 A163738 A190987 * A277441 A307021 A197083 Adjacent sequences: A233735 A233736 A233737 * A233739 A233740 A233741 KEYWORD nonn,easy AUTHOR Tim Fulford, Dec 15 2013 EXTENSIONS More terms from Vincenzo Librandi, Dec 16 2013 STATUS approved

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Last modified May 24 15:25 EDT 2024. Contains 372778 sequences. (Running on oeis4.)