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Binomial transform of A083579.
2

%I #10 Dec 28 2023 23:26:00

%S 0,1,3,10,34,114,374,1202,3798,11842,36550,111954,340982,1034210,

%T 3127206,9434866,28419286,85503618,257035142,772219538,2319017910,

%U 6962034466,20896589158,62711787570,188181500054,564640969154

%N Binomial transform of A083579.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,12).

%F a(n) = 2*3^n/3-5*0^n/12-(n+1)*2^(n-2).

%F G.f.: x*(1-4*x+5*x^2)/((1-2*x)^2*(1-3*x)). - _Colin Barker_, Apr 16 2012

%e a(0) = 2/3-5/12-1/4 = 0 (use 0^0=1).

%t CoefficientList[Series[x*(1 - 4*x + 5*x^2)/((1 - 2*x)^2*(1 - 3*x)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Dec 28 2023 *)

%Y Cf. A083579.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 01 2003