%I #20 Jan 30 2020 21:29:15
%S 1,2,4,16,64,224,800,3008,11392,43008,163328,624640,2397696,9227264,
%T 35608576,137764864,534102016,2074394624,8069922816,31440338944,
%U 122652655616,479052693504,1873097261056,7331070869504,28718945140736
%N Expansion of 1/sqrt(1-4x+4x^2-16x^3).
%C In general, a(n)=sum{k=0..floor(n/2), C(2k,k)C(2(n-2k),n-2k)*r^k} has g.f. 1/sqrt(1-4x-4r*x^2+16r*x^3).
%H Vincenzo Librandi, <a href="/A106186/b106186.txt">Table of n, a(n) for n = 0..200</a>
%H Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Szalay/szalay42.html">Diagonal Sums in the Pascal Pyramid, II: Applications</a>, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
%F a(n)=sum{k=0..floor(n/2), C(2k, k)C(2(n-2k), n-2k)*(-1)^k}.
%F D-finite with recurrence: n*a(n)+2(1-2n)*a(n-1) +4(n-1)*a(n-2)+8(3-2n)*a(n-3)=0. - _R. J. Mathar_, Dec 08 2011
%F a(n) ~ 2^(2*n+1)/sqrt(5*Pi*n). - _Vaclav Kotesovec_, Feb 01 2014
%t CoefficientList[Series[1/Sqrt[1-4x+4x^2-16x^3],{x,0,30}],x] _Harvey P. Dale_, May 17 2012
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 24 2005