%I #29 Aug 16 2024 20:41:16
%S 0,5,200,3375,40000,390625,3375000,26796875,200000000,1423828125,
%T 9765625000,64990234375,421875000000,2681884765625,16748046875000,
%U 102996826171875,625000000000000,3748321533203125,22247314453125000
%N a(n) = n^3 * 5^n.
%C Subsequence of A047486. [_Bruno Berselli_, Feb 07 2013]
%H Vincenzo Librandi, <a href="/A128791/b128791.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 (20,-150,500,-625).
%F G.f.: 5*x*(1+20*x+25*x^2)/(1-5*x)^4. - _Vincenzo Librandi_ Feb 07 2013
%F a(n) = 20*a(n-1) - 150*a(n-2) + 500*a(n-3) - 625*a(n-4). - _Vincenzo Librandi_, Feb 09 2013
%t CoefficientList[Series[5 x (1 + 20 x + 25 x^2)/(1-5 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 07 2013 *)
%t LinearRecurrence[{20,-150,500,-625},{0,5,200,3375},20] (* _Harvey P. Dale_, Aug 16 2024 *)
%o (Magma) [n^3*5^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 07 2013
%o (Magma) I:=[0, 5, 200, 3375]; [n le 4 select I[n] else 20*Self(n-1)-150*Self(n-2)+500*Self(n-3)-625*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Feb 09 2013
%Y Cf. A036289, A007758.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Apr 07 2007