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%I #19 Jan 30 2020 21:29:16
%S 1,2,4,9,24,68,204,642,2096,7026,24026,83454,293562,1043488,3741954,
%T 13520253,49171485,179859763,661240417,2442023860,9055315765,
%U 33701442548,125845246605,471346884115,1770306347204,6665954191204,25159152509961
%N Expansion (1-sqrt(1-4*x))/(2*(1-x^4-x)).
%H G. C. Greubel, <a href="/A200966/b200966.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{i=0..(n-1)} (Sum_{j=0..(i/3)} binomial(i-3*j,j))*binomial(2*(n-i)-2,n-i-1))/(n-i)), n>0.
%F D-finite with recurrence: n*a(n) +n*a(n-1) +2*(30-13n)*a(n-2) +12*(2n-5)*a(n-3) -n*a(n-4) -2n*a(n-5) +12*(2n-5)*a(n-6)=0. - _R. J. Mathar_, Nov 26 2011
%F a(n) ~ 2^(2*n+6) / (191*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jan 31 2014
%t Rest[CoefficientList[Series[(1-Sqrt[1-4x])/(2(1-x^4-x)),{x,0,40}],x]] (* _Harvey P. Dale_, May 08 2013 *)
%o (Maxima)
%o a(n):=sum(((sum(binomial(i-3*j,j),j,0,i/3))*binomial(2*(n-i)-2,n-i-1))/(n-i),i,0,n-1);
%o (PARI) x='x+O('x^50); Vec((1-sqrt(1-4*x))/(2*(1-x^4-x))) \\ _G. C. Greubel_, May 27 2017
%K nonn
%O 1,2
%A _Vladimir Kruchinin_, Nov 25 2011
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