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

0,2

Comments

Hankel transform of A158495.

Links

Table of n, a(n) for n=0..66.

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

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]

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 *)

Prog

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

Crossrefs

Cf. A019425.

Sequence in context: A319296 A211779 A318445 * A265722 A019425 A255242

Adjacent sequences: A158493 A158494 A158495 * A158497 A158498 A158499

Keyword

easy,sign

Author

Paul Barry, Mar 20 2009

Status

approved