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

Author

Paul Barry, Feb 23 2009

Keywords

• easy
• sign

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).

Programs

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 *)

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

Formula

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