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%I #29 Sep 02 2024 15:38:30
%S 8,192,2304,20480,153600,1032192,6422528,37748736,212336640,
%T 1153433600,6090129408,31406948352,158779572224,789200240640,
%U 3865470566400,18691697672192,89369679495168,423037098786816,1984618488135680,9235897673318400,42669847250731008,195836215046438912
%N a(n) = (n^3 + n^2)*4^n.
%H Vincenzo Librandi, <a href="/A129004/b129004.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 (16,-96,256,-256).
%F G.f.: 8*x*(1+8*x)/(1-4*x)^4. - _R. J. Mathar_, Dec 19 2008
%F a(1)=8, a(2)=192, a(3)=2304, a(4)=20480, a(n)=16*a(n-1)-96*a(n-2)+ 256*a(n-3)-256*a(n-4). - _Harvey P. Dale_, May 12 2011
%F a(n) = 8*(A038846(n-1)+8*A038846(n-2)), with A038846(-1)=0. - _Bruno Berselli_, Feb 12 2013
%F E.g.f.: 8*exp(4*x)*x*(1 + 8*x + 8*x^2). - _Stefano Spezia_, Sep 02 2024
%t Table[(n^3+n^2)4^n,{n, 20}] (* or *) LinearRecurrence[{16,-96,256,-256}, {8,192,2304,20480},20] (* _Harvey P. Dale_, May 12 2011 *)
%o (Magma) [(n^3+n^2)*4^n: n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%Y Cf. A036289, A038846, A128796.
%K nonn,easy
%O 1,1
%A _Mohammad K. Azarian_, May 01 2007