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A127630 Expansion of (1+x-x^2-x^3)/(1+x^2)^2. 3
1, 1, -3, -3, 5, 5, -7, -7, 9, 9, -11, -11, 13, 13, -15, -15, 17, 17, -19, -19, 21, 21, -23, -23, 25, 25, -27, -27, 29, 29, -31, -31, 33, 33, -35, -35, 37, 37, -39, -39, 41, 41, -43, -43, 45, 45, -47, -47, 49, 49, -51, -51, 53, 53, -55, -55 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform of A045621(n+1).

LINKS

Table of n, a(n) for n=0..55.

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

FORMULA

a(n) = (-1)^binomial(n,2) * ( 2*floor(n/2)+1 ).

a(n) = (n + 1 - (n mod 2))*(-1)^floor(n/2). [Wesley Ivan Hurt, Jun 30 2013]

G.f.:  1/(G(0) - x), where G(k) = x*(2*k+1) - (2*k-1)/( 1 + x/( 1 - x*(2*k+3)/G(k+1) )); (continued fraction ). - Sergei N. Gladkovskii, Dec 27 2013

CROSSREFS

Cf. A109613.

Sequence in context: A117767 A293701 A296063 * A267458 A109613 A063196

Adjacent sequences:  A127627 A127628 A127629 * A127631 A127632 A127633

KEYWORD

sign,easy

AUTHOR

Paul Barry, Jan 20 2007

STATUS

approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)