OFFSET
1,2
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).
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)
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)
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 *)
PROG
(Magma) [(n^3-n)*5^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Apr 28 2007
EXTENSIONS
Offset corrected by Mohammad K. Azarian, Nov 20 2008
STATUS
approved