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%I #12 May 27 2013 02:31:18
%S 1,1,2,7,38,250,1748,12463,89606,647710,4702844,34286038,250928732,
%T 1843209556,13586564072,100479347647,745418148806,5546324817718,
%U 41382983725292,309586136922898,2321772733668980,17453199438926188,131489046194284568,992678648890643206
%N Sequence with Hankel transform equal to 3^floor(n^2/2).
%C Hankel transform is A168493 (a trivial Somos-4 sequence linked to y^2=1-16x+76x^2-96x^3).
%H Vincenzo Librandi, <a href="/A168492/b168492.txt">Table of n, a(n) for n = 0..300</a>
%F G.f.: 1/(1-x/(1-x/(1-3x/(1-3x/(1-x/(1-x/(1-3x/(1-3x/(1-x/(1-x/(1-3x/(1-.... (continued fraction);
%F G.f.: 1/(1-x-x^2/(1-4x-9x^2/(1-4x-x^2/(1-4x-9x^2/(1-4x-x^2/(1-4x-9x^2/(1-... (continued fraction);
%F G.f.: (1-2*x-sqrt((1-2*x)*(1-14*x+48*x^2)))/(6*x*(1-2*x)).
%F Recurrence: (n+1)*a(n) = 2*(8*n-3)*a(n-1) - 4*(19*n-31)*a(n-2) + 48*(2*n-5)* a(n-3). - _Vaclav Kotesovec_, Oct 20 2012
%F a(n) ~ 2^(3*n+1)/(3*sqrt(3*Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 20 2012
%F a(n) = Sum_{k, 0<=k<=n} A168511(n,k)*3^(n-k). - _Philippe Deléham_, Mar 19 2013
%t CoefficientList[Series[(1-2*x-Sqrt[(1-2*x)(1-14*x+48*x^2)])/(6*x*(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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