A131386 a(n) = (-1)^n*n*(n-2).

1, 0, -3, 8, -15, 24, -35, 48, -63, 80, -99, 120, -143, 168, -195, 224, -255, 288, -323, 360, -399, 440, -483, 528, -575, 624, -675, 728, -783, 840, -899, 960, -1023, 1088, -1155, 1224, -1295, 1368, -1443, 1520, -1599, 1680, -1763, 1848, -1935, 2024, -2115, 2208, -2303, 2400

Offset: 1

Author

Jamel Ghanouchi, Aug 26 2008

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• P. Barry, A. Hennessy, Meixner-Type Results for Riordan Arrays and Associated Integer Sequences, J. Int. Seq. 13 (2010) # 10.9.4, section 9.
• Index entries for linear recurrences with constant coefficients, signature (-3,-3,-1).

Crossrefs

Cf. A067998.

Programs

Magma

[(-1)^n*n*(n-2): n in [1..50]]; // Vincenzo Librandi, Jul 09 2012

Mathematica

Table[(-1)^n*n*(n - 2), {n, 80}] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2012 *)
CoefficientList[Series[(1+3*x)/(1+x)^3,{x,0,50}],x] (* Vincenzo Librandi, Jul 09 2012 *)
LinearRecurrence[{-3,-3,-1},{1,0,-3},50] (* Harvey P. Dale, Aug 25 2023 *)

PARI

Vec(x*(1+3*x)/(1+x)^3 + O(x^100)) \\ Altug Alkan, Dec 19 2015

Formula

From R. J. Mathar, Dec 07 2009: (Start)

a(n) = -3*a(n-1) - 3*a(n-2) - a(n-3).

G.f.: x*(1+3*x)/(1+x)^3. (End)

Sum_{n>2} 1/a(n) = -1/4. - Enrique Pérez Herrero, Dec 19 2015

Extensions

Entry completely rewriten by Jamel Ghanouchi, Nov 02 2009

Terms corrected by Jamel Ghanouchi, Nov 07 2009

Definition clarified; zeros skipped; sequence extended - R. J. Mathar, Dec 07 2009