cp's OEIS Frontend

A128963 a(n) = (n^3 - n)*5^n.

%I A128963 #26 Oct 02 2022 10:32:52
%S A128963 0,150,3000,37500,375000,3281250,26250000,196875000,1406250000,
%T A128963 9667968750,64453125000,418945312500,2666015625000,16662597656250,
%U A128963 102539062500000,622558593750000,3735351562500000,22178649902343750,130462646484375000,761032104492187500
%N A128963 a(n) = (n^3 - n)*5^n.
%H A128963 Vincenzo Librandi, <a href="/A128963/b128963.txt">Table of n, a(n) for n = 1..1000</a>
%H A128963 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-150,500,-625).
%F A128963 a(1)=0, a(2)=150, a(3)=3000, a(4)=37500, a(n)=20*a(n-1)-150*a(n-2)+ 500*a(n-3)- 625*a(n-4). - _Harvey P. Dale_, Jul 22 2012
%F A128963 G.f.: 150*x^2/(1 - 5*x)^4. - _Vincenzo Librandi_, Feb 12 2013
%F A128963 a(n) = 150*A081143(n+1). - _Bruno Berselli_, Feb 12 2013
%F A128963 From _Amiram Eldar_, Oct 02 2022: (Start)
%F A128963 a(n) = A007531(n+1)*A000351(n).
%F A128963 Sum_{n>=2} 1/a(n) = (8/5)*log(5/4) - 7/20.
%F A128963 Sum_{n>=2} (-1)^n/a(n) = (18/5)*log(6/5) - 13/20. (End)
%t A128963 Table[(n^3-n)5^n,{n,20}] (* or *) LinearRecurrence[{20,-150,500,-625},{0,150,3000,37500},20] (* _Harvey P. Dale_, Jul 22 2012 *)
%t A128963 CoefficientList[Series[150 x/(1 - 5 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 12 2013 *)
%o A128963 (Magma) [(n^3-n)*5^n: n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%Y A128963 Cf. A000351, A007531, A036289, A081143, A128796.
%Y A128963 Cf. A128960, A128961, A128962, A128964, A128965, A128967, A128969.
%K A128963 nonn,easy
%O A128963 1,2
%A A128963 _Mohammad K. Azarian_, Apr 28 2007
%E A128963 Offset corrected by _Mohammad K. Azarian_, Nov 20 2008