A167386 a(n) = (-1)^n*n*(n+1)*(2*n-5)/6.

1, -1, -2, 10, -25, 49, -84, 132, -195, 275, -374, 494, -637, 805, -1000, 1224, -1479, 1767, -2090, 2450, -2849, 3289, -3772, 4300, -4875, 5499, -6174, 6902, -7685, 8525, -9424, 10384, -11407, 12495, -13650, 14874, -16169, 17537, -18980, 20500, -22099, 23779

Offset: 1

Author

Jamel Ghanouchi, Nov 02 2009

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (-4,-6,-4,-1).

Programs

Magma

[(-1)^n*n*(n+1)*(2*n-5)/6: n in [1..50]]; // Vincenzo Librandi, Aug 25 2011

Mathematica

Table[n (-1)^n*(n + 1) (2*n - 5)/6, {n, 60}] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)

PARI

a(n)=(-1)^n*n*(n+1)*(2*n-5)/6 \\ Charles R Greathouse IV, Aug 24 2011

Formula

a(n) = -4*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4).

G.f.: x*(1+3*x)/(1+x)^4.

Extensions

Note that for a sequence in which every other term is zero, the OEIS policy is to omit those zeros. - N. J. A. Sloane, Nov 08 2009

Zeros removed by skipping even-indexed polynomials - R. J. Mathar, Nov 12 2009