|
%I #37 Aug 25 2023 19:11:33
%S 1,0,-3,8,-15,24,-35,48,-63,80,-99,120,-143,168,-195,224,-255,288,
%T -323,360,-399,440,-483,528,-575,624,-675,728,-783,840,-899,960,-1023,
%U 1088,-1155,1224,-1295,1368,-1443,1520,-1599,1680,-1763,1848,-1935,2024,-2115,2208,-2303,2400
%N a(n) = (-1)^n*n*(n-2).
%H Vincenzo Librandi, <a href="/A131386/b131386.txt">Table of n, a(n) for n = 1..1000</a>
%H P. Barry, A. Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Barry5/barry96s.html">Meixner-Type Results for Riordan Arrays and Associated Integer Sequences</a>, J. Int. Seq. 13 (2010) # 10.9.4, section 9.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-3,-1).
%F From _R. J. Mathar_, Dec 07 2009: (Start)
%F a(n) = -3*a(n-1) - 3*a(n-2) - a(n-3).
%F G.f.: x*(1+3*x)/(1+x)^3. (End)
%F Sum_{n>2} 1/a(n) = -1/4. - _Enrique Pérez Herrero_, Dec 19 2015
%t Table[(-1)^n*n*(n - 2), {n, 80}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2012 *)
%t CoefficientList[Series[(1+3*x)/(1+x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 09 2012 *)
%t LinearRecurrence[{-3,-3,-1},{1,0,-3},50] (* _Harvey P. Dale_, Aug 25 2023 *)
%o (Magma) [(-1)^n*n*(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jul 09 2012
%o (PARI) Vec(x*(1+3*x)/(1+x)^3 + O(x^100)) \\ _Altug Alkan_, Dec 19 2015
%Y Cf. A067998.
%K sign,easy
%O 1,3
%A _Jamel Ghanouchi_, Aug 26 2008
%E Entry completely rewriten by _Jamel Ghanouchi_, Nov 02 2009
%E Terms corrected by _Jamel Ghanouchi_, Nov 07 2009
%E Definition clarified; zeros skipped; sequence extended - _R. J. Mathar_, Dec 07 2009
|
