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%I #25 Sep 08 2022 08:45:30
%S 10,250,3750,42500,406250,3468750,27343750,203125000,1441406250,
%T 9863281250,65527343750,424804687500,2697753906250,16833496093750,
%U 103454589843750,627441406250000,3761291503906250,22315979003906250
%N a(n) = (n^3 +n)*5^n.
%H Vincenzo Librandi, <a href="/A128013/b128013.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-150,500,-625).
%F G.f.: 10*x(1+5*x+25*x^2)/(1-5*x)^4. - _Vincenzo Librandi_, Feb 22 2013
%F a(n) = 20*a(n-1) -150*a(n-2) +500*a(n-3) -625*a(n-4). - _Vincenzo Librandi_, Feb 23 2013
%t Table[(n^3 + n) 5^n, {n, 30}] (* or *) CoefficientList[Series[10 (1 + 5 x + 25 x^2)/(1 - 5 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 22 2013 *)
%o (Magma) [(n^3 + n)*5^n: n in [1..20]]; // _Vincenzo Librandi_, Feb 22 2013
%o (Magma) I:=[10,250,3750,42500]; [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..20]]; // _Vincenzo Librandi_, Feb 23 2013
%o (PARI) for(n=1, 30, print1((n^3 +n)*5^n, ", ")) \\ _G. C. Greubel_, May 08 2018
%Y Cf. A128796, A128960, A128985, A129002.
%K nonn,easy
%O 1,1
%A _Mohammad K. Azarian_, May 02 2007