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%I #12 Apr 30 2014 01:29:21
%S 1,3,12,50,211,895,3805,16193,68940,293526,1249622,5318976,22634700,
%T 96296410,409573584,1741574006,7403616923,31466106703,133704121665,
%U 568008916093,2412570019447,10245302874071,43500597657111,184670002546295,783850164628721,3326671128027805,14116630429874265
%N Sum_{i=0..n} C(2n+i,n-i).
%C Apparently a bisection of A026847.
%C Row sums of A159965. - _Paul Barry_, Apr 28 2009
%H Vincenzo Librandi, <a href="/A108080/b108080.txt">Table of n, a(n) for n = 0..200</a>
%F From _Paul Barry_, Apr 28 2009: (Start)
%F G.f.: x/(x*sqrt(1-4x)-(1-2x-(1-3x)*c(x))), c(x) the g.f. of A000108.
%F a(n) = Sum_{k=0..n} Sum_{j=0..n} C(n+k,j-k)*C(n,j). (End)
%F From _Paul Barry_, Sep 07 2009: (Start)
%F G.f.: (1/sqrt(1-4x))*(1/(1-xc(x)^3)), c(x) the g.f. of A000108.
%F a(n) = Sum_{k=0..n} C(2n,n-k)*F(k+1) = Sum_{k=0..n} C(2n,k)*F(n-k+1).
%F a(n) = Sum_{k=0..n} C(2k,k) * A165201(n-k). (End)
%F Recurrence: n*(17*n-93)*a(n) = 4*(34*n^2 - 189*n + 98)*a(n-1) - 5*(51*n^2 - 271*n + 252)*a(n-2) - 4*(17*n^2 - 184*n + 406)*a(n-3) + 44*(2*n-7) * a(n-4). - _Vaclav Kotesovec_, Oct 24 2012
%F a(n) ~ 1/2*(1+1/sqrt(5))*(sqrt(5)+2)^n. - _Vaclav Kotesovec_, Oct 24 2012
%t CoefficientList[Series[x/(x*Sqrt[1-4*x]-(1-2*x-(1-3*x)*(1-Sqrt[1-4*x])/(2*x))), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 24 2012 *)
%o (PARI) x='x+O('x^66); Vec(x/(x*sqrt(1-4*x)-(1-2*x-(1-3*x)*(1-sqrt(1-4*x))/(2*x)))) \\ _Joerg Arndt_, May 15 2013
%K nonn
%O 0,2
%A _Ralf Stephan_, Jun 03 2005
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