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%I #21 Sep 08 2022 08:45:30
%S 0,8,256,4608,65536,819200,9437184,102760448,1073741824,10871635968,
%T 107374182400,1039382085632,9895604649984,92908732547072,
%U 862017116176384,7916483719987200,72057594037927936,650770146155036672
%N n^2*8^n.
%C Subsequence of A047351. [_Bruno Berselli_, Feb 07 2013]
%H Vincenzo Librandi, <a href="/A128787/b128787.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (24,-192,512).
%F G.f.: 8*x*(1 + 8*x)/(1 - 8*x)^3. - _Vincenzo Librandi_, Feb 06 2013
%F a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3). - _Vincenzo Librandi_, Feb 06 2013
%e a(1) = 1^2 * 8^1 = 1 * 8 = 8.
%e a(2) = 2^2 * 8^2 = 4 * 64 = 256.
%e a(3) = 3^2 * 8^3 = 9 * 512 = 4608.
%t LinearRecurrence[{24, -192, 512}, {0, 8, 256}, 30] (* or *) CoefficientList[Series[8 x (1 + 8 x)/((1 - 8 x)^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 06 2013 *)
%t Table[n^2 8^n, {n, 0, 19}] (* _Alonso del Arte_, Feb 06 2013 *)
%o (Magma) [n^2*8^n: n in [0..20]]; // _Vincenzo Librandi_, Feb 06 2013
%Y Cf. A036289, A007758.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Apr 07 2007