A128967 a(n) = (n^3-n)*8^n.

0, 384, 12288, 245760, 3932160, 55050240, 704643072, 8455716864, 96636764160, 1063004405760, 11338713661440, 117922622078976, 1200666697531392, 12006666975313920, 118219490218475520, 1148417904979476480, 11024811887802974208, 104735712934128254976

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 (32,-384,2048,-4096).

Crossrefs

Cf. A001018, A007531, A036289, A128796, A140802.

Cf. A128960, A128961, A128962, A128963, A128964, A128965, A128969.

Programs

Magma

[(n^3 - n)*8^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

Mathematica

LinearRecurrence[{32, -384, 2048, -4096}, {0, 384, 12288, 245760}, 30] (* Vincenzo Librandi, Feb 11 2013 *)

Formula

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

G.f.: 384x^2/(1-8x)^4.

a(n) = 384*A140802(n-2). (End)

a(n) = 32*a(n-1) - 384*a(n-2) + 2048*a(n-3) - 4096*a(n-4). - Vincenzo Librandi, Feb 11 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A001018(n).

Sum_{n>=2} 1/a(n) = (49/16)*log(8/7) - 13/32.

Sum_{n>=2} (-1)^n/a(n) = (81/16)*log(9/8) - 19/32. (End)

Extensions

Corrected the offset. - Mohammad K. Azarian, Nov 20 2008