A128985 - OEIS

%I #26 Jan 30 2025 16:45:17

%S 0,16,144,768,3200,11520,37632,114688,331776,921600,2478080,6488064,

%T 16613376,41746432,103219200,251658240,606076928,1443889152,

%U 3406823424,7969177600,18496880640,42630905856,97626619904,222264557568

%N a(n) = (n^3 - n^2)*2^n.

%H Vincenzo Librandi, <a href="/A128985/b128985.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).

%F G.f.: 16*x^2*(1 + x)/(1 - 2*x)^4. - _Vincenzo Librandi_, Feb 11 2013

%F a(n) = 8*a(n-1) -24*a(n-2) +32*a(n-3) -16*a(n-4). - _Vincenzo Librandi_, Feb 11 2013

%t CoefficientList[Series[16 x (1+x)/(1 - 2 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 11 2013 *)

%t Table[(n^3-n^2)2^n,{n,30}] (* or *) LinearRecurrence[{8,-24,32,-16},{0,16,144,768},30] (* _Harvey P. Dale_, Jul 06 2014  *)

%o (Magma) [(n^3-n^2)*2^n: n in [1..25]]; // _Vincenzo Librandi_, Feb 11 2013

%o (Magma) I:=[0, 16, 144, 768]; [n le 4 select I[n] else 8*Self(n-1) - 24*Self(n-2) + 32*Self(n-3) - 16*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Feb 11 2013

%o (PARI) a(n)=(n^3-n^2)<<n \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A128796, A036289.

%K nonn,easy

%O 1,2

%A _Mohammad K. Azarian_, Apr 30 2007

%E Offset corrected by _Mohammad K. Azarian_, Nov 19 2008