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%I #6 May 27 2012 12:24:15
%S 1,-1,0,1,1,-4,-1,11,2,-35,-1,112,-9,-369,66,1237,-327,-4212,1433,
%T 14527,-5926,-50659,23749,178356,-93427,-633225,363342,2264885,
%U -1402803,-8154564,5390861,29534183,-20655948,-107538835,79005679,393462584,-301884895,-1445937945,1153012596,5335046209
%N Expansion of 1/(sqrt(1+4x^2)+x(1-x)).
%C Diagonal sums of number triangle A111963.
%F a(n)=sum{k=0..floor(n/2), sum{i=0..floor((n-k)/2), C(2i+2k-n-1, k)C(2i+k-n-1)(-1)^(n-k)*4^i}}
%t CoefficientList[Series[1/(Sqrt[1+4x^2]+x(1-x)),{x,0,40}],x] (* _Harvey P. Dale_, May 27 2012 *)
%K easy,sign
%O 0,6
%A _Paul Barry_, Aug 23 2005
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