A129005 a(n) = (n^3 + n^2)*5^n.

0, 10, 300, 4500, 50000, 468750, 3937500, 30625000, 225000000, 1582031250, 10742187500, 70898437500, 457031250000, 2888183593750, 17944335937500, 109863281250000, 664062500000000, 3968811035156250, 23483276367187500

Offset: 0

Author

Mohammad K. Azarian, May 01 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 (20,-150,500,-625).

Crossrefs

Cf. A036289, A081143, A128796.

Programs

Magma

[(n^3+n^2)*5^n: n in [0..25]]; // Vincenzo Librandi, Feb 12 2013

Magma

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

Mathematica

CoefficientList[Series[10 x (1 + 10 x)/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)
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 *)

PARI

A129005(n)=5^n*(1+n)*n^2 \\ - M. F. Hasler, Feb 12 2013

Formula

G.f.: 10*x*(1 + 10*x)/(1 - 5*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 20*a(n-1)-150*a(n-2)+500*a(n-3)-625*a(n-4). - Vincenzo Librandi, Feb 12 2013

a(n) = 10*A081143(n+2)+100*A081143(n+1). - Bruno Berselli, Feb 13 2013

Extensions

Initial term a(0)=0 added by M. F. Hasler, Feb 12 2013