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 A116396 Expansion of 2/((2+x)*sqrt(1-4*x)-x). 1

%I

%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)}}.

%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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