A128962 a(n) = (n^3 - n)*4^n.

0, 96, 1536, 15360, 122880, 860160, 5505024, 33030144, 188743680, 1038090240, 5536481280, 28789702656, 146565758976, 732828794880, 3607772528640, 17523466567680, 84112639524864, 399535037743104, 1880164883496960, 8774102789652480, 40637949762600960

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 (16,-96,256,-256).

Crossrefs

Cf. A000302, A007531, A036289, A128796.

Cf. A128960, A128961, A128963, A128964, A128965, A128967, A128969.

Programs

Magma

[(n^3-n)*4^n: n in [1..20]]; // Vincenzo Librandi, Feb 09 2013

Mathematica

CoefficientList[Series[96 x / (1-4 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 09 2013 *)
Table[(n^3-n)4^n,{n,20}] (* or *) LinearRecurrence[{16,-96,256,-256},{0,96,1536,15360},20] (* Harvey P. Dale, Dec 31 2018 *)

Formula

G.f.: 96*x^2/(1-4*x)^4. - Vincenzo Librandi, Feb 09 2013

a(n) = 16*a(n-1) - 96*a(n-2) + 256*a(n-3) - 256*a(n-4). - Vincenzo Librandi, Feb 09 2013

a(n) = 96*A038846(n-2) for n>1. - Bruno Berselli, Feb 10 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A000302(n).

Sum_{n>=2} 1/a(n) = (9/8)*log(4/3) - 5/16.

Sum_{n>=2} (-1)^n/a(n) = (25/8)*log(5/4) - 11/16. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008