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A118969 2*binomial(5*n+1,n)/(4*n+2). 8

%I

%S 1,2,11,80,665,5980,56637,556512,5620485,57985070,608462470,

%T 6474009360,69682358811,757366074080,8300675584120,91634565938880,

%U 1018002755977245,11372548404732930,127677890035721025,1439777493407492640

%N 2*binomial(5*n+1,n)/(4*n+2).

%C A quadrisection of A118968.

%C If y=x+2*x^3+x^5, the series reversion is x=y -2*y^3 +11*y^5 -80*y^7 +665*y^9 -... - _R. J. Mathar_, Sep 29 2012

%H Vincenzo Librandi, <a href="/A118969/b118969.txt">Table of n, a(n) for n = 0..100</a>

%H Karol A. Penson and Karol Zyczkowski, <a href="http://dx.doi.org/10.1103/PhysRevE.83.061118">Product of Ginibre matrices: Fuss-Catalan and Raney distribution</a>, <a href="http://arxiv.org/abs/1103.3453/">arXiv version</a>

%F a(n) is sum of top row terms in M^n, where M is an infinite square production matrix with the tetrahedral series in each column, as follows:

%F 1, 1, 0, 0, 0, 0,...

%F 4, 1, 1, 0, 0, 0,...

%F 10, 10, 4, 1, 0, 0,...

%F 20, 20, 10, 4, 1, 0,...

%F 35, 35, 20, 10, 4, 1,...

%F ... - _Gary W. Adamson_, Aug 11 2011

%F G.f.: hypergeom([1/5, 2/5, 3/5, 4/5],[1/2, 3/4, 5/4],3125*x/256)^2 - _Mark van Hoeij_, Apr 19 2013

%F a(n) = 2*binomial(5n+1,n-1)/n for n>0, a(0)=1. [_Bruno Berselli_, Jan 19 2014]

%F 8*n*(4*n+1)*(2*n+1)*(4*n-1)*a(n) -5*(5*n+1)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - _R. J. Mathar_, Oct 10 2014

%e a(3) = 80 = sum of top row terms in M^n, = (35 + 35 + 9 + 1)

%t Table[2*Binomial[5n+1,n]/(4n+2),{n,0,20}] (* _Harvey P. Dale_, Aug 21 2011 *)

%o (MAGMA) [2*Binomial(5*n+1,n)/(4*n+2): n in [0..20]]; // _Vincenzo Librandi_, Aug 12 2011

%o (PARI) a(n)=2*binomial(5*n+1,n)/(4*n+2); \\ _Joerg Arndt_, Apr 20 2013

%K nonn,easy

%O 0,2

%A _Paul Barry_, May 07 2006

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)