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%I #22 Sep 08 2022 08:45:30
%S 0,144,3888,62208,777600,8398080,82301184,752467968,6530347008,
%T 54419558400,438984437760,3448023220224,26487087464448,
%U 199671890116608,1481082701414400,10833062044631040,78268873272459264
%N a(n) = (n^3 - n^2)*6^n.
%H Vincenzo Librandi, <a href="/A128989/b128989.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 (24,-216,864,-1296).
%F G.f.: 144*x^2*(1+3*x)/(1-6*x)^4. - _Vincenzo Librandi_, Feb 12 2013
%F a(n) = 24*a(n-1)-216*a(n-2)+864*a(n-3)-1296*a(n-4). - _Vincenzo Librandi_, Feb 12 2013
%t CoefficientList[Series[144 x (1 + 3 x)/(1 - 6 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 12 2013 *)
%t Table[(n^3-n^2)6^n,{n,20}] (* or *) LinearRecurrence[{24,-216,864,-1296},{0,144,3888,62208},20] (* _Harvey P. Dale_, Apr 29 2019 *)
%o (Magma) [(n^3-n^2)*6^n: n in [1..25]]; /* or */ I:=[0,144,3888,62208]; [n le 4 select I[n] else 24*Self(n-1)-216*Self(n-2)+864*Self(n-3)-1296*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%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 20 2008
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