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%I #10 Jan 30 2020 21:29:15
%S 1,3,12,48,194,787,3199,13017,52997,215831,879076,3580511,14582842,
%T 59388280,241829963,984609111,4008282780,16315179752,66399357417,
%U 270193396769,1099323033137,4472155924094,18190769442979,73982564102230
%N Expansion of (1/((1-4x)c(x)))/(1-x^2c(x)/sqrt(1-4x)), c(x) the g.f. of A000108.
%C Diagonal sums of A113955.
%F G.f.: (1+sqrt(1-4x))/(sqrt(1-4x)(sqrt(1-4x)(x+2)-x)); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(j, j-k)C(2n-2k, n-k-j)}}.
%F Conjecture D-finite with recurrence: n*a(n) +2*(-5*n+4)*a(n-1) +(27*n-46)*a(n-2) +(5*n-2)*a(n-3) +(-57*n+188)*a(n-4) +2*(-21*n+83)*a(n-5) +4*(-2*n+9)*a(n-6)=0. - _R. J. Mathar_, Jan 24 2020
%t CoefficientList[Series[(1+Sqrt[1-4x])/(2-x(7+Sqrt[1-4x]+4x)),{x,0,30}],x] (* _Harvey P. Dale_, Feb 10 2015 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 09 2005
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