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A127630
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Expansion of (1+x-x^2-x^3)/(1+x^2)^2.
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3
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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
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = (-1)^binomial(n,2) * ( 2*floor(n/2)+1 ).
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
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MATHEMATICA
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CoefficientList[Series[(1+x-x^2-x^3)/(1+x^2)^2, {x, 0, 100}], x] (* or *) LinearRecurrence[{0, -2, 0, -1}, {1, 1, -3, -3}, 100] (* Harvey P. Dale, Nov 18 2020 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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