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%I #12 Oct 28 2020 13:26:19
%S 1,10,38,108,270,632,1426,3148,6854,14784,31674,67508,143278,303016,
%T 638882,1343388,2817942,5898128,12320650,25689988,53477246,111148920,
%U 230686578,478150508,989855590,2046820192,4227858266,8724152148,17985175374,37044092744
%N Sum{(k+1)*T(n,2n-k)}, 0<=k<=2n, T given by A027960.
%H Colin Barker, <a href="/A027982/b027982.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F From _Colin Barker_, Nov 25 2014: (Start)
%F a(n) = (-10+11*2^n+2*(-3+2^n)*n).
%F a(n) = 6*a(n-1)-13*a(n-2)+12*a(n-3)-4*a(n-4).
%F G.f.: -(2*x^3+9*x^2-4*x-1) / ((x-1)^2*(2*x-1)^2).
%F (End)
%t LinearRecurrence[{6,-13,12,-4},{1,10,38,108},40] (* _Harvey P. Dale_, Oct 28 2020 *)
%o (PARI) Vec(-(2*x^3+9*x^2-4*x-1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ _Colin Barker_, Nov 25 2014
%K nonn,easy
%O 0,2
%A _Clark Kimberling_
%E More terms from _Colin Barker_, Nov 25 2014
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