A128964 a(n) = (n^3-n)*6^n.

0, 216, 5184, 77760, 933120, 9797760, 94058496, 846526464, 7255941120, 59861514240, 478892113920, 3735358488576, 28524555730944, 213934167982080, 1579821548175360, 11510128422420480, 82872924641427456, 590469588070170624, 4168020621671792640, 29176144351702548480

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 (24,-216,864,-1296).

Crossrefs

Cf. A000400, A007531, A036289, A081144, A128796.

Cf. A128960, A128961, A128962, A128963, A128965, A128967, A128969.

Programs

Magma

[(n^3-n)*6^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

Magma

I:=[0, 216, 5184, 77760]; [n le 4 select I[n] else 24*Self(n-1) -216*Self(n-2) +864*Self(n-3) -1296*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

Mathematica

CoefficientList[Series[216 x/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2013 *)

Formula

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

G.f.: 216*x^2/(1-6*x)^4.

a(n) = 216*A081144(n+1). (End)

a(n) = 24*a(n-1) - 216*a(n-2) + 864*a(n-3) - 1296*a(n-4). - Vincenzo Librandi, Feb 11 2013

From Amiram Eldar, Jan 04 2022: (Start)

Sum_{n>=2} 1/a(n) = 25*log(6/5)/12 - 3/8.

Sum_{n>=2} (-1)^n/a(n) = 49*log(7/6)/12 - 5/8. (End)

a(n) = A007531(n+1)*A000400(n). - Amiram Eldar, Oct 02 2022

Extensions

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