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A233738
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2*binomial(5*n+10, n)/(n+2).
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6
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1, 10, 95, 920, 9135, 92752, 959595, 10084360, 107375730, 1156073100, 12565671261, 137702922560, 1519842008360, 16880051620320, 188519028884675, 2115822959020080, 23851913523156675, 269958280013904870, 3066451080298820830, 34946186787944832400
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OFFSET
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0,2
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COMMENTS
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Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=5, r=10.
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LINKS
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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.
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FORMULA
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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
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MAPLE
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A233738:=n->2*binomial(5*n+10, n)/(n+2): seq(A233738(n), n=0..30); # Wesley Ivan Hurt, Sep 07 2014
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MATHEMATICA
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Table[2 Binomial[5 n + 10, n]/(n + 2), {n, 0, 40}] (* Vincenzo Librandi, Dec 16 2013 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Tim Fulford, Dec 15 2013
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EXTENSIONS
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More terms from Vincenzo Librandi, Dec 16 2013
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STATUS
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approved
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