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

Author

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

Keywords

• easy
• sign

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).

Crossrefs

Cf. A016757.

Programs

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 *)

PARI

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

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