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

0, 150, 3000, 37500, 375000, 3281250, 26250000, 196875000, 1406250000, 9667968750, 64453125000, 418945312500, 2666015625000, 16662597656250, 102539062500000, 622558593750000, 3735351562500000, 22178649902343750, 130462646484375000, 761032104492187500

Offset: 1

Author

Mohammad K. Azarian, Apr 28 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-150,500,-625).

Crossrefs

Cf. A000351, A007531, A036289, A081143, A128796.

Cf. A128960, A128961, A128962, A128964, A128965, A128967, A128969.

Programs

Magma

[(n^3-n)*5^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

Mathematica

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 *)
CoefficientList[Series[150 x/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)

Formula

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

G.f.: 150*x^2/(1 - 5*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 150*A081143(n+1). - Bruno Berselli, Feb 12 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A000351(n).

Sum_{n>=2} 1/a(n) = (8/5)*log(5/4) - 7/20.

Sum_{n>=2} (-1)^n/a(n) = (18/5)*log(6/5) - 13/20. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008