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a(n) = n*(n-1)*6^n.
1

%I #18 Jan 20 2024 16:43:40

%S 0,0,72,1296,15552,155520,1399680,11757312,94058496,725594112,

%T 5441955840,39907676160,287335268352,2037468266496,14262277865472,

%U 98738846760960,677066377789440,4604051368968192,31077346740535296

%N a(n) = n*(n-1)*6^n.

%H Vincenzo Librandi, <a href="/A128800/b128800.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-108,216).

%F G.f.: 72*x^2/(1 - 6*x)^3. - _Vincenzo Librandi_, Feb 11 2013

%F a(n) = 72*A081136(n). - _R. J. Mathar_, Apr 26 2015

%F a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3). - _Wesley Ivan Hurt_, Jan 20 2024

%t CoefficientList[Series[72 x^2/(1 - 6 x)^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 11 2013 *)

%t LinearRecurrence[{18,-108,216},{0,0,72},30] (* _Harvey P. Dale_, Mar 22 2018 *)

%o (Magma) [(n^2-n)*6^n: n in [0..25]]; // _Vincenzo Librandi_, Feb 11 2013

%Y Cf. A036289, A007758.

%K nonn,easy

%O 0,3

%A _Mohammad K. Azarian_, Apr 07 2007