A128964 - OEIS

%I #27 Oct 02 2022 10:32:57

%S 0,216,5184,77760,933120,9797760,94058496,846526464,7255941120,

%T 59861514240,478892113920,3735358488576,28524555730944,

%U 213934167982080,1579821548175360,11510128422420480,82872924641427456,590469588070170624,4168020621671792640,29176144351702548480

%N a(n) = (n^3-n)*6^n.

%H Vincenzo Librandi, <a href="/A128964/b128964.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24,-216,864,-1296).

%F From _R. J. Mathar_, Dec 19 2008: (Start)

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

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

%F a(n) = 24*a(n-1) - 216*a(n-2) + 864*a(n-3) - 1296*a(n-4). - _Vincenzo Librandi_, Feb 11 2013

%F From _Amiram Eldar_, Jan 04 2022: (Start)

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

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

%F a(n) = A007531(n+1)*A000400(n). - _Amiram Eldar_, Oct 02 2022

%t CoefficientList[Series[216 x/(1 - 6 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 11 2013 *)

%o (Magma) [(n^3-n)*6^n: n in [0..25]]; (* or *) 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

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

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

%K nonn,easy

%O 1,2

%A _Mohammad K. Azarian_, Apr 28 2007

%E Corrected offset. - _Mohammad K. Azarian_, Nov 20 2008