A105811 Expansion of g.f. (1+x-x^2)/(1+x)^2.

1, -1, 0, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32, 33, -34, 35, -36, 37, -38, 39, -40, 41, -42, 43, -44, 45, -46, 47, -48, 49, -50, 51, -52, 53, -54, 55, -56, 57, -58, 59, -60, 61, -62, 63, -64, 65

Offset

0,5

Comments

First column of number triangle A105810.

Links

Table of n, a(n) for n=0..67.

Index entries for linear recurrences with constant coefficients, signature (-2,-1).

Formula

a(n) = -0^n-(-1)^n*(n-2).

E.g.f.: exp(-x)*(2 + x) - 1. - Stefano Spezia, Dec 29 2024

Mathematica

CoefficientList[Series[(1+x-x^2)/(1+x)^2, {x, 0, 70}], x] (* or *) LinearRecurrence[ {-2, -1}, {1, -1, 0}, 70] (* Harvey P. Dale, Jun 16 2016 *)

Prog

(PARI) a(n)=-0^n-(-1)^n*(n-2) \\ Charles R Greathouse IV, Sep 02 2015

Crossrefs

Cf. A105810.

Sequence in context: A001478 A001489 A038608 * A209662 A272813 A258070

Adjacent sequences: A105808 A105809 A105810 * A105812 A105813 A105814

Keyword

easy,sign

Author

Paul Barry, May 04 2005

Status

approved