A128960 a(n) = (n^3 - n)*2^n.

0, 24, 192, 960, 3840, 13440, 43008, 129024, 368640, 1013760, 2703360, 7028736, 17891328, 44728320, 110100480, 267386880, 641728512, 1524105216, 3586129920, 8367636480, 19377684480, 44568674304, 101871255552, 231525580800, 523449139200, 1177760563200, 2638183661568

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 (8,-24,32,-16).

Crossrefs

Cf. A000079, A007531, A036289, A128796.

Cf. A128961, A128962, A128963, A128964, A128965, A128967, A128969.

Programs

Magma

[(n^3-n)*2^n: n in [1..25]]; /* or */ I:=[0,24,192,960]; [n le 4 select I[n] else 8*Self(n-1)-24*Self(n-2)+32*Self(n-3)-16*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

Mathematica

CoefficientList[Series[24 x/(1 - 2 x)^4, {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -24, 32, -16}, {0, 24, 192, 960}, 30] (* Vincenzo Librandi, Feb 12 2013 *)

PARI

a(n)=(n^3-n)<Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 24*x^2/(1-2*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Vincenzo Librandi, Feb 12 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A000079(n).

Sum_{n>=2} 1/a(n) = (2*log(2)-1)/8.

Sum_{n>=2} (-1)^n/a(n) = (3/2)^2*log(3/2) - 7/8. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 19 2008