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%I #13 Aug 19 2022 04:20:06
%S 1,2,4,12,40,128,408,1328,4384,14560,48576,162816,547936,1850048,
%T 6263680,21257856,72298240,246345728,840775424,2873802240,9835840512,
%U 33704557568,115622041600,397032488960,1364610270720,4694145256448
%N Expansion of 1/sqrt((1-2x)^2-8x^3).
%C In general, 1/sqrt((1-a*x)^2-4*b*x^3) expands to sum{k=0..floor(n/2), C(n-k,k)C(n-2k,k)b^k*a^(n-3k)}.
%H Michael De Vlieger, <a href="/A113179/b113179.txt">Table of n, a(n) for n = 0..1837</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(n-k, k)C(n-2k, k)2^(n-2k)}.
%F D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. [Belbachir]
%t CoefficientList[Series[1/Sqrt[(1-2x)^2-8x^3],{x,0,30}],x] (* _Harvey P. Dale_, Dec 23 2017 *)
%Y Cf. A098479.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 16 2005
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