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%I #9 Jun 06 2014 15:30:35
%S 1,3,13,63,325,1748,9685,54841,315605,1838610,10811788,64041706,
%T 381525253,2283436938,13718099275,82672421423,499546587317,
%U 3025336228390,18357852413062,111587292429820,679306584310220
%N Expansion of log'(1/2-sqrt((5*x+2*sqrt(1-4*x)-2)/x)/2).
%F a(n) = sum(k=0..n, binomial(2*k-1,k)*binomial(2*n,n-k)).
%F a(n) ~ 5^(2*n+1/2) / (sqrt(3*Pi*n) * 2^(2*n+1)). - _Vaclav Kotesovec_, Jun 06 2014
%t Table[Sum[Binomial[2 i - 1, i] Binomial[2 n, n - i], {i, 0, n}], {n,
%t 0, 20}] (* _Wesley Ivan Hurt_, Jun 06 2014 *)
%o (Maxima)
%o a(n):=sum(binomial(2*k-1,k)*binomial(2*n,n-k),k,0,n);
%K nonn
%O 0,2
%A _Vladimir Kruchinin_, Jun 02 2014
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