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%I #4 Mar 30 2012 18:55:30
%S 1,2,4,10,28,82,264,866,2984,10476,37500,135916,496242,1821384,
%T 6712394,24818020,92016874,342043052,1274461144,4759439600,
%U 17812520318,66803249358,251038475982,945202437760,3565529448118,13474452634994,51010511291144,193438196953970
%N Binomial convolution of the Floor-Sqrt transform of Catalan numbers.
%F a(n) = sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)/(k+1)))*floor(sqrt(binomial(2*n-2*k,n-k)/(n-k+1))),k=0..n).
%t Table[Sum[Binomial[n,k]Floor[Sqrt[Binomial[2k,k]/(k+1)]]Floor[Sqrt[Binomial[2n-2k,n-k]/(n-k+1)]],{k,0,n}],{n,0,100}]
%o (Maxima) makelist(sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)/(k+1)))*floor(sqrt(binomial(2*n-2*k,n-k)/(n-k+1))),k,0,n),n,0,24);
%K nonn
%O 0,2
%A _Emanuele Munarini_, Jul 07 2011
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