A128791 a(n) = n^3 * 5^n.

0, 5, 200, 3375, 40000, 390625, 3375000, 26796875, 200000000, 1423828125, 9765625000, 64990234375, 421875000000, 2681884765625, 16748046875000, 102996826171875, 625000000000000, 3748321533203125, 22247314453125000

Offset: 0

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

• nonn
• easy

Comments

Subsequence of A047486. [Bruno Berselli, Feb 07 2013]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-150,500,-625).

Crossrefs

Cf. A036289, A007758.

Programs

Magma

[n^3*5^n: n in [0..30]]; // Vincenzo Librandi, Feb 07 2013

Magma

I:=[0, 5, 200, 3375]; [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..30]]; // Vincenzo Librandi, Feb 09 2013

Mathematica

CoefficientList[Series[5 x (1 + 20 x + 25 x^2)/(1-5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 07 2013 *)
LinearRecurrence[{20,-150,500,-625},{0,5,200,3375},20] (* Harvey P. Dale, Aug 16 2024 *)

Formula

G.f.: 5*x*(1+20*x+25*x^2)/(1-5*x)^4. - Vincenzo Librandi Feb 07 2013

a(n) = 20*a(n-1) - 150*a(n-2) + 500*a(n-3) - 625*a(n-4). - Vincenzo Librandi, Feb 09 2013