A128969 - OEIS

%I #26 Jan 30 2025 17:36:34

%S 0,486,17496,393660,7085880,111602610,1607077584,21695547384,

%T 278942752080,3451916556990,41422998683880,484649084601396,

%U 5551434969070536,62453643402043530,691794203838020640,7560322370515511280,81651481601567521824,872650209616752889494

%N a(n) = (n^3 - n)*9^n.

%H Vincenzo Librandi, <a href="/A128969/b128969.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 (36,-486,2916,-6561).

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

%F G.f.: 486x^2/(1-9x)^4.

%F a(n) = 486*A038291(n+1,3). (End)

%F a(n) = 36*a(n-1) - 486*a(n-2) + 2916*a(n-3) - 6561*a(n-4). - _Vincenzo Librandi_, Feb 11 2013

%F From _Amiram Eldar_, Oct 02 2022: (Start)

%F a(n) = A007531(n+1)*A001019(n).

%F Sum_{n>=2} 1/a(n) = (32/9)*log(9/8) - 5/12.

%F Sum_{n>=2} (-1)^n/a(n) = (50/9)*log(10/9) - 7/12. (End)

%t CoefficientList[Series[486 x/(1 - 9 x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 11 2013 *)

%o (Magma) [(n^3-n)*9^n: n in [0..25]]; // _Vincenzo Librandi_, Feb 11 2013

%o (Magma) I:=[0, 486, 17496, 393660]; [n le 4 select I[n] else 36*Self(n-1) - 486*Self(n-2) + 2916*Self(n-3) - 6561*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Feb 11 2013

%Y Cf. A001019, A007531, A036289, A038291, A128796.

%Y Cf. A128960, A128961, A128962, A128963, A128964, A128965, A128967.

%K nonn,easy

%O 1,2

%A _Mohammad K. Azarian_, Apr 28 2007

%E Offset corrected by _Mohammad K. Azarian_, Nov 20 2008