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%I #4 Mar 30 2012 18:55:30
%S 1,2,6,20,72,270,1040,4036,15714,61226,238778,930716,3628520,14143922,
%T 55134174,214941488,838158510,3269630046,12761106790,49834920864,
%U 194743761948,761543265544,2980128724806,11670402459630,45734346816026,179348093549914,703781965002650
%N Binomial convolution of the Floor-Sqrt transform of central binomial coefficients.
%F a(n) = sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)))*floor(sqrt(binomial(2*n-2*k,n-k))),k=0..n).
%t Table[Sum[Binomial[n,k]Floor[Sqrt[Binomial[2k,k]]]Floor[Sqrt[Binomial[2n-2k,n-k]]],{k,0,n}],{n,0,100}]
%o (Maxima) makelist(sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)))*floor(sqrt(binomial(2*n-2*k,n-k))),k,0,n),n,0,24);
%K nonn
%O 0,2
%A _Emanuele Munarini_, Jul 07 2011