A128799 a(n) = n*(n-1)*5^n.

0, 0, 50, 750, 7500, 62500, 468750, 3281250, 21875000, 140625000, 878906250, 5371093750, 32226562500, 190429687500, 1110839843750, 6408691406250, 36621093750000, 207519531250000, 1167297363281250, 6523132324218750

Offset: 0

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-75,125).

Crossrefs

Cf. A007758, A036289, A081135.

Programs

Magma

[(n^2-n)*5^n: n in [0..20]]; // Vincenzo Librandi, Feb 10 2013

Maple

seq(5^n*n*(n-1), n=0..30); # G. C. Greubel, May 17 2021

Mathematica

CoefficientList[Series[50x^2/(1-5x)^3, {x, 0, 30}] ,x] (* Vincenzo Librandi, Feb 10 2013 *)
Table[n(n-1)5^n,{n,0,30}] (* or *) LinearRecurrence[{15,-75,125},{0,0,50},30] (* Harvey P. Dale, Nov 05 2019 *)

Sage

[2*5^n*binomial(n,2) for n in (0..30)] # G. C. Greubel, May 17 2021

Formula

G.f.: 50*x^2/(1 - 5*x)^3. - Vincenzo Librandi, Feb 10 2013

a(n) = 50*A081135(n). - R. J. Mathar, Apr 26 2015

E.g.f.: 25*x^2*exp(5*x). - G. C. Greubel, May 17 2021

a(n) = 15*a(n-1) - 75*a(n-2) + 125*a(n-3). - Wesley Ivan Hurt, May 17 2021