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A098337 Expansion of 1/sqrt(1-4x+20x^2).

%I A098337 #26 Jan 30 2020 21:29:15
%S A098337 1,2,-4,-40,-80,352,2624,3712,-32000,-186880,-134144,2885632,13520896,
%T A098337 -1269760,-256000000,-966164480,1056112640,22286827520,66722201600,
%U A098337 -162411315200,-1901125959680,-4329895362560
%N A098337 Expansion of 1/sqrt(1-4x+20x^2).
%C A098337 Central coefficients of (1+2x-4x^2)^n. Binomial transform of A098334.
%H A098337 Vincenzo Librandi, <a href="/A098337/b098337.txt">Table of n, a(n) for n = 0..200</a>
%H A098337 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.
%H A098337 Tony D. Noe, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html">On the Divisibility of Generalized Central Trinomial Coefficients</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F A098337 E.g.f.: exp(2x)BesselI(0, 4*I*x), I=sqrt(-1);
%F A098337 a(n) = sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)2^n(-1)^k};
%F A098337 a(n) = sum{k=0..n, binomial(2k, k)binomial(k, n-k)(-5)^(n-k)}.
%F A098337 a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)binomial(2(n-k), n)(-5)^k. - _Paul Barry_, Sep 08 2004.
%F A098337 D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +20*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 24 2012
%F A098337 Lim sup n->infinity |a(n)|^(1/n) = 2*sqrt(5). - _Vaclav Kotesovec_, Feb 08 2014
%t A098337 Table[Sum[Binomial[n,k]*Binomial[2*(n-k), n]*(-5)^k,{k,0,Floor[n/2]}],{n,0,20}] (* _Vaclav Kotesovec_, Feb 08 2014 *)
%t A098337 CoefficientList[Series[1/Sqrt[1-4x+20x^2],{x,0,30}],x] (* _Harvey P. Dale_, Jul 29 2015 *)
%K A098337 easy,sign
%O A098337 0,2
%A A098337 _Paul Barry_, Sep 03 2004