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%I #25 Sep 08 2022 08:45:30
%S 0,10,300,4500,50000,468750,3937500,30625000,225000000,1582031250,
%T 10742187500,70898437500,457031250000,2888183593750,17944335937500,
%U 109863281250000,664062500000000,3968811035156250,23483276367187500
%N (n^3+n^2)*5^n.
%H Vincenzo Librandi, <a href="/A129005/b129005.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.: 10*x*(1 + 10*x)/(1 - 5*x)^4. - _Vincenzo Librandi_, Feb 12 2013
%F a(n) = 20*a(n-1)-150*a(n-2)+500*a(n-3)-625*a(n-4). - _Vincenzo Librandi_, Feb 12 2013
%F a(n) = 10*A081143(n+2)+100*A081143(n+1). [_Bruno Berselli_, Feb 13 2013]
%t CoefficientList[Series[10 x (1 + 10 x)/(1 - 5 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 12 2013 *)
%t Table[(n^3+n^2)5^n,{n,0,30}] (* or *) LinearRecurrence[{20,-150,500,-625},{0,10,300,4500},30] (* _Harvey P. Dale_, May 15 2022 *)
%o (Magma) [(n^3+n^2)*5^n: n in [0..25]]; /* or */ I:=[0,10,300,4500]; [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..25]]; // _Vincenzo Librandi_, Feb 12 2013
%o (PARI) A129005(n)=5^n*(1+n)*n^2 \\ - _M. F. Hasler_, Feb 12 2013
%Y Cf. A036289, A081143, A128796.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, May 01 2007
%E Initial term a(0)=0 added by _M. F. Hasler_, Feb 12 2013
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