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%I #11 Jan 30 2020 21:29:15
%S 1,1,1,5,13,25,65,181,445,1113,2945,7685,19821,51865,136513,358229,
%T 942109,2487385,6573825,17387045,46066253,122213913,324512833,
%U 862511605,2294698109,6109933657,16280439937,43411979845,115835462445
%N Expansion of 1/sqrt((1-x)^2-8x^3).
%C 1/sqrt((1-x)^2-4rx^3) expands to sum{k=0..floor(n/2), binomial(n-k,k)binomial(n-2k,k)r^k}
%H Michael De Vlieger, <a href="/A098480/b098480.txt">Table of n, a(n) for n = 0..2309</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), binomial(n-k, k)binomial(n-2k, k)2^k}. D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. - _R. J. Mathar_, Nov 10 2014
%t Array[Sum[Binomial[# - k, k] Binomial[# - 2 k, k] 2^k, {k, 0, #/2}] &, 29, 0] (* _Michael De Vlieger_, Jul 16 2019 *)
%Y Cf. A098479, A098481.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Sep 10 2004
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