A129006 a(n) = (n^3 + n^2)*6^n.

12, 432, 7776, 103680, 1166400, 11757312, 109734912, 967458816, 8162933760, 66512793600, 526781325312, 4074936532992, 30901602041856, 230390642442240, 1692665944473600, 12277470317248512, 88052482431516672

Offset: 1

Author

Mohammad K. Azarian, May 01 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. A128796, A036289.

Programs

Magma

[(n^3+n^2)*6^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

Magma

I:=[12,432,7776,103680]; [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 12 2013

Mathematica

CoefficientList[Series[12 (1 + 12 x)/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)
Table[(n^3+n^2)6^n,{n,20}] (* or *) LinearRecurrence[{24,-216,864,-1296},{12,432,7776,103680},20] (* Harvey P. Dale, Aug 16 2014 *)

Formula

G.f.: 12*x*(1+12*x)/(1-6*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 24*a(n-1)-216*a(n-2)+864*a(n-3)-1296*a(n-4). - Vincenzo Librandi, Feb 12 2013