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%I #18 Apr 17 2014 06:53:40
%S 1,6,31,150,699,3178,14198,62604,273235,1182786,5085666,21743956,
%T 92522206,392066340,1655432524,6967724312,29245179267,122442487474,
%U 511487386730,2132341655556,8873167793578,36861311739308,152895342950196,633290273209000,2619653638855214,10823294835350388
%N Self-convolution of Sum(binomial(2*n, i), i=0..n).
%H Fung Lam, <a href="/A240879/b240879.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f. = (g.f. of A032443)^2.
%F n*a(n) = 32*(2*n-3)*a(n-3) + 48*(1-n)*a(n-2) + 6*(2*n-1)*a(n-1).
%F Asymptotics: a(n) ~ 2^(2*n)*((n+2)/4 + sqrt(n/Pi)).
%F Recurrence: (n-2)*n*a(n) = 2*n*(4*n-7)*a(n-1) - 8*(n-1)*(2*n-1)*a(n-2). - _Vaclav Kotesovec_, Apr 16 2014
%t CoefficientList[Series[((1/Sqrt[1-4*x] + 1/(1-4*x))/2)^2, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 16 2014 *)
%Y Cf. A032443.
%K nonn
%O 0,2
%A _Fung Lam_, Apr 13 2014
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