A128969 a(n) = (n^3 - n)*9^n.

0, 486, 17496, 393660, 7085880, 111602610, 1607077584, 21695547384, 278942752080, 3451916556990, 41422998683880, 484649084601396, 5551434969070536, 62453643402043530, 691794203838020640, 7560322370515511280, 81651481601567521824, 872650209616752889494

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 (36,-486,2916,-6561).

Crossrefs

Cf. A001019, A007531, A036289, A038291, A128796.

Cf. A128960, A128961, A128962, A128963, A128964, A128965, A128967.

Programs

Magma

[(n^3-n)*9^n: n in [0..25]]; // Vincenzo Librandi, Feb 11 2013

Magma

I:=[0, 486, 17496, 393660]; [n le 4 select I[n] else 36*Self(n-1) - 486*Self(n-2) + 2916*Self(n-3) - 6561*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

Mathematica

CoefficientList[Series[486 x/(1 - 9 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2013 *)

Formula

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

G.f.: 486x^2/(1-9x)^4.

a(n) = 486*A038291(n+1,3). (End)

a(n) = 36*a(n-1) - 486*a(n-2) + 2916*a(n-3) - 6561*a(n-4). - Vincenzo Librandi, Feb 11 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A001019(n).

Sum_{n>=2} 1/a(n) = (32/9)*log(9/8) - 5/12.

Sum_{n>=2} (-1)^n/a(n) = (50/9)*log(10/9) - 7/12. (End)

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008