%I #17 Jul 28 2022 21:43:13

%S 1,4,19,75,264,869,2741,8396,25175,74271,216336,623689,1782889,

%T 5060500,14277019,40070259,111954456,311555501,863978525,2388417116,

%U 6584117471,18104432199,49667825184,135974484625,371543306449,1013443026724

%N Expansion of (1-2x+6x^2-x^3)/(1-3x+x^2)^2.

%C Hankel transform of A054109.

%H G. C. Greubel, <a href="/A167478/b167478.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,-11,6,-1).

%F G.f.: (1-2*x+6*x^2-x^3)/(1-3*x+x^2)^2.

%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Jul 28 2022

%t LinearRecurrence[{6, -11, 6, -1}, {1, 4, 19, 75}, 100] (* _G. C. Greubel_, Jun 13 2016 *)

%t CoefficientList[Series[(1-2x+6x^2-x^3)/(1-3x+x^2)^2,{x,0,30}],x] (* _Harvey P. Dale_, Aug 04 2018 *)

%Y Cf. A054109.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Nov 04 2009