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%I #8 Jan 30 2020 21:29:15
%S 1,2,7,25,93,353,1358,5273,20614,81003,319584,1264924,5019743,
%T 19963699,79541181,317406302,1268283199,5073605801,20316709251,
%U 81427911966,326612013623,1310968893954,5265285993860,21158914176719,85071253608611
%N Expansion of 2/((2+x)*sqrt(1-4*x)-x).
%C Diagonal sums of number triangle A116395.
%C Diagonal sums of the Riordan matrix ((1-sqrt(1-4x))/(2x*sqrt(1-4x)),(1-sqrt(1-4x))/(2*sqrt(1-4x))) (A035324) [Emanuele Munarini, Apr 26 2011]
%F a(n)=sum{k=0..floor(n/2), (4^(n-k)/2^k)*sum{j=0..k, C(k,j)C(n-k+(j-1)/2,n-k)(-1)^(k-j)}}.
%F D-finite with recurrence: +2*n*a(n) +(-13*n+10)*a(n-1) +(9*n-16)*a(n-2) +2*(19*n-41)*a(n-3) +(23*n-66)*a(n-4) +2*(2*n-7)*a(n-5)=0. - _R. J. Mathar_, Jan 24 2020
%t CoefficientList[Series[(x+(2+x)Sqrt[1-4x])/(2-6x-8x^2-2x^3),{x,0,25}],x]) [Emanuele Munarini, Apr 26 2011]
%K easy,nonn
%O 0,2
%A _Paul Barry_, Feb 12 2006
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