A165935 a(n) = (-1)^(n-1)*n*(4n^2-5)^2.

1, -242, 2883, -13924, 45125, -115926, 255367, -504008, 915849, -1560250, 2523851, -3912492, 5853133, -8495774, 12015375, -16613776, 22521617, -30000258, 39343699, -50880500

Offset

1,2

Comments

These are the partial sums of the alternating series of odd fifth powers beginning with 1. See A016757.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (-6,-15,-20,-15,-6,-1).

Formula

G.f.: x*(1-236*x+1446*x^2-236*x^3+x^4) / (1+x)^6. - R. J. Mathar, Nov 27 2011

E.g.f.: x*(1 - 120*x + 360*x^2 - 160*x^3 + 16*x^4)*exp(-x). - Ilya Gutkovskiy, Apr 17 2016

Mathematica

Table[(-1)^(n - 1)*n*(4*n^2 - 5)^2, {n, 1, 50}] (* G. C. Greubel, Apr 18 2016 *)
LinearRecurrence[{-6, -15, -20, -15, -6, -1}, {1, -242, 2883, -13924, 45125, -115926}, 20] (* Harvey P. Dale, Mar 24 2020 *)

Prog

(PARI) vector(100, n, (-1)^(n-1)*n*(4*n^2-5)^2) \\ Altug Alkan, Apr 18 2016

Crossrefs

Cf. A016757.

Sequence in context: A258886 A354563 A354565 * A318529 A006601 A283723

Adjacent sequences: A165932 A165933 A165934 * A165936 A165937 A165938

Keyword

easy,sign

Author

Richard L. Peterson (rl_pete(AT)yahoo.com), Oct 01 2009

Status

approved