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%I #11 May 27 2013 02:38:11
%S 1,1,2,6,24,112,560,2888,15136,80160,427968,2300736,12445440,67702272,
%T 370205184,2033976960,11224014336,62186741248,345825348608,
%U 1929744008192,10802203119616,60644473282560,341383505977344
%N Sequence with Hankel transform equal to 2^floor(n^2/2).
%C Hankel transform is A099202 (a trivial Somos-4 sequence linked to y^2=1-12x+44x^2-48x^3.
%H Vincenzo Librandi, <a href="/A168490/b168490.txt">Table of n, a(n) for n = 0..300</a>
%F G.f.: 1/(1-x/(1-x/(1-2x/(1-2x/(1-x/(1-x/(1-2x/(1-2x/(1-x/(1-x/(1-2x/(1-.... (continued fraction);
%F G.f.: 1/(1-x-x^2/(1-3x-4x^2/(1-3x-x^2/(1-3x-4x^2/(1-3x-x^2/(1-3x-4x^2/(1-... (continued fraction);
%F G.f.: (1-2x-sqrt((1-2x)(1-10x+24x^2)))/(4x(1-2x)).
%F Recurrence: (n+1)*a(n) = 4*(3*n-1)*a(n-1) - 4*(11*n-17)*a(n-2) + 24*(2*n-5)*a(n-3). - _Vaclav Kotesovec_, Oct 20 2012
%F a(n) ~ 2^(n-5/2)*3^(n+1)/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 20 2012
%F a(n) = Sum_{k, 0<=k<=n} A168511(n,k)*2^(n-k). - _Philippe Deléham_, Mar 19 2013
%t CoefficientList[Series[(1-2*x-Sqrt[(1-2*x)(1-10*x+24*x^2)])/(4x*(1-2*x)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 20 2012 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Nov 27 2009
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