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%I #12 Jan 30 2020 21:29:16
%S 1,2,4,10,28,96,354,1372,5512,22740,95768,410016,1779210,7807724,
%T 34589432,154488460,694883528,3144917888,14311109396,65439770904,
%U 300534169744,1385612474536,6410981989808,29757955549888,138534010818650,646663905140300
%N Expansion of 2-sqrt(1-4*x-4*x^2-4*x^3)
%F a(n)=2*sum(k=1..n, (binomial(2*k-2,k-1) * sum(j=0..k, binomial(j,n-3*k+2*j) * binomial(k,j) ) )/k ), n>0, a(0)=1.
%F D-finite with recurrence: n*a(n) +2*(-2*n+3)*a(n-1) +4*(-n+3)*a(n-2) +2*(-2*n+9)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2020
%o (Maxima)
%o a(n):=2*sum((binomial(2*k-2,k-1)*sum(binomial(j,n-3*k+2*j)*binomial(k,j),j,0,k))/k,k,1,n);
%K nonn
%O 0,2
%A _Vladimir Kruchinin_, Jun 03 2011
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