A158496 Expansion of (1-4x+x^2)/(1+x^2)^2.

1, -4, -1, 8, 1, -12, -1, 16, 1, -20, -1, 24, 1, -28, -1, 32, 1, -36, -1, 40, 1, -44, -1, 48, 1, -52, -1, 56, 1, -60, -1, 64, 1, -68, -1, 72, 1, -76, -1, 80, 1, -84, -1, 88, 1, -92, -1, 96, 1, -100, -1, 104, 1, -108, -1, 112, 1, -116, -1, 120, 1, -124, -1, 128, 1, -132, -1

Offset: 0

Author

Paul Barry, Mar 20 2009

Keywords

• easy
• sign

Comments

Hankel transform of A158495.

Links

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

Crossrefs

Cf. A019425.

Programs

Mathematica

CoefficientList[Series[(1-4x+x^2)/(1+x^2)^2,{x,0,70}],x] (* or *) LinearRecurrence[{0,-2,0,-1},{1,-4,-1,8},70] (* Harvey P. Dale, Mar 06 2012 *)

PARI

Vec((1-4*x+x^2)/(1+x^2)^2 + O(x^100)) \\ Altug Alkan, Jan 10 2016

Formula

a(n) = (n+3/2-(n+1/2)*(-1)^n)*(-1)^C(n+1,2).

a(0)=1, a(1)=-4, a(2)=-1, a(3)=8, a(n) = -2*a(n-2)-a(n-4). - Harvey P. Dale, Mar 06 2012