A157128 Expansion of (1 - x - x^2 + x^3 - x^5) / ((1 + x)^2*(1 - x + x^2)^2).

1, -1, -1, -1, 2, 1, 1, -3, -1, -1, 4, 1, 1, -5, -1, -1, 6, 1, 1, -7, -1, -1, 8, 1, 1, -9, -1, -1, 10, 1, 1, -11, -1, -1, 12, 1, 1, -13, -1, -1, 14, 1, 1, -15, -1, -1, 16, 1, 1, -17, -1, -1, 18, 1, 1, -19, -1, -1, 20, 1, 1

Offset

0,5

Comments

Hankel transform of A157127.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,-2,0,0,-1).

Formula

a(n) = -2*a(n-3) - a(n-6) for n>5. - Colin Barker, Oct 23 2019

Mathematica

CoefficientList[Series[(1-x-x^2+x^3-x^5)/(1+2x^3+x^6), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 0, -2, 0, 0, -1}, {1, -1, -1, -1, 2, 1}, 70] (* Harvey P. Dale, Jul 08 2019 *)

Prog

(PARI) Vec((1 - x - x^2 + x^3 - x^5) / ((1 + x)^2*(1 - x + x^2)^2) + O(x^80)) \\ Colin Barker, Oct 23 2019

Crossrefs

Sequence in context: A210873 A224838 A030272 * A359899 A301376 A307828

Adjacent sequences: A157125 A157126 A157127 * A157129 A157130 A157131

Keyword

easy,sign

Author

Paul Barry, Feb 23 2009

Status

approved