%I #33 Sep 02 2024 15:37:04

%S 0,0,8,48,192,640,1920,5376,14336,36864,92160,225280,540672,1277952,

%T 2981888,6881280,15728640,35651584,80216064,179306496,398458880,

%U 880803840,1937768448,4244635648,9261023232,20132659200,43620761600,94220845056,202937204736,435939180544

%N a(n) = n*(n-1)*2^n.

%H Vincenzo Librandi, <a href="/A128796/b128796.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).

%F G.f.: 8*x^2/(1 - 2*x)^3. - _Vincenzo Librandi_, Feb 10 2013

%F a(n) = 8*A001788(n-1). - _R. J. Mathar_, Apr 26 2015

%F From _Amiram Eldar_, Jul 11 2020: (Start)

%F Sum_{n>=2} 1/a(n) = (1 - log(2))/2.

%F Sum_{n>=2} (-1)^n/a(n) = (3*log(3/2) - 1)/2. (End)

%F E.g.f.: 4*exp(2*x)*x^2. - _Stefano Spezia_, Sep 02 2024

%t CoefficientList[Series[8 x^2/(1 - 2 x)^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 10 2013 *)

%o (Magma) [(n^2-n)*2^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 10 2013

%o (PARI) a(n)=n*(n-1)<<n \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A001788, A007758, A036289.

%K nonn,easy

%O 0,3

%A _Mohammad K. Azarian_, Apr 07 2007