A128965 a(n) = (n^3 - n)*7^n.

0, 294, 8232, 144060, 2016840, 24706290, 276710448, 2905459704, 29054597040, 279650496510, 2610071300760, 23751648836916, 211605598728888, 1851548988877770, 15951806673408480, 135590356723972080, 1138958996481365472, 9467596658251350486, 77968443067952298120

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 (28,-294,1372,-2401).

Crossrefs

Cf. A000420, A007531, A036289, A128796, A140107.

Cf. A128960, A128961, A128962, A128963, A128964, A128967, A128969.

Programs

Magma

[(n^3 - n)*7^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

Mathematica

LinearRecurrence[{28, -294, 1372, -2401}, {0, 294, 8232, 144060}, 30] (* Vincenzo Librandi, Feb 11 2013 *)
Table[(n^3-n)7^n,{n,20}] (* Harvey P. Dale, May 14 2020 *)

Formula

From R. J. Mathar, Dec 19 2008: (Start)

G.f.: 294x^2/(1-7x)^4.

a(n) = 294*A140107(n-2). (End)

a(n) = 28*a(n-1) - 294*a(n-2) + 1372*a(n-3) - 2401*a(n-4). - Vincenzo Librandi, Feb 11 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A000420(n).

Sum_{n>=2} 1/a(n) = (18/7)*log(7/6) - 11/28.

Sum_{n>=2} (-1)^n/a(n) = (32/7)*log(8/7) - 17/28. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008