A128989 a(n) = (n^3 - n^2)*6^n.
0, 144, 3888, 62208, 777600, 8398080, 82301184, 752467968, 6530347008, 54419558400, 438984437760, 3448023220224, 26487087464448, 199671890116608, 1481082701414400, 10833062044631040, 78268873272459264, 559392241329635328, 3959619590588203008, 27786804144478617600
Offset: 1
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).
Programs
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Magma
[(n^3-n^2)*6^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
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Magma
I:=[0,144,3888,62208]; [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
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Mathematica
CoefficientList[Series[144 x (1 + 3 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},{0,144,3888,62208},20] (* Harvey P. Dale, Apr 29 2019 *)
Formula
From Vincenzo Librandi, Feb 12 2013: (Start)
G.f.: 144*x^2*(1+3*x)/(1-6*x)^4.
a(n) = 24*a(n-1)-216*a(n-2)+864*a(n-3)-1296*a(n-4). (End)
E.g.f.: 72*exp(6*x)*x^2*(1 + 3*x). - Stefano Spezia, Mar 08 2025
Extensions
Offset corrected by Mohammad K. Azarian, Nov 20 2008