A128792 - OEIS

%I #20 Mar 12 2023 13:35:43

%S 0,6,288,5832,82944,972000,10077696,96018048,859963392,7346640384,

%T 60466176000,482882881536,3761479876608,28694344753152,

%U 215031266279424,1586874322944000,11555266180939776,83160677851987968

%N n^3*6^n.

%H Vincenzo Librandi, <a href="/A128792/b128792.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (24,-216,864,-1296).

%F G.f.: 6*x*(1 + 24*x + 36*x^2)/(1 - 6*x)^4. - _Vincenzo Librandi_, Feb 08 2013

%F a(n) = 24*a(n-1) - 216*a(n-2) + 864*a(n-3) - 1296*a(n-4). - _Vincenzo Librandi_, Feb 09 2013

%t CoefficientList[Series[6 x *(1+24 x + 36 x^2)/(1-6*x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 08 2013 *)

%t LinearRecurrence[{24,-216,864,-1296},{0,6,288,5832},20] (* _Harvey P. Dale_, Mar 12 2023 *)

%o (Magma) [n^3*6^n: n in [0..20]]; // _Vincenzo Librandi_, Feb 08 2013

%o (Magma) I:=[0, 6, 288, 5832]; [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..30]]; // _Vincenzo Librandi_, Feb 09 2013

%Y Cf. A036289, A007758.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Apr 07 2007