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A100052
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A Chebyshev transform of the odd numbers.
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0
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1, 3, 3, -2, -9, -9, 2, 15, 15, -2, -21, -21, 2, 27, 27, -2, -33, -33, 2, 39, 39, -2, -45, -45, 2, 51, 51, -2, -57, -57, 2, 63, 63, -2, -69, -69, 2, 75, 75, -2, -81, -81, 2, 87, 87, -2, -93, -93, 2, 99, 99, -2, -105, -105, 2, 111, 111, -2, -117, -117
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A Chebyshev transform of A005408: if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
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FORMULA
| G.f.: (1-x^2)(1+x+x^2)/(1-x+x^2)^2; a(n)=2a(n-1)-3a(n-2)+2a(n-3)-a(n-4); a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)*(2(n-2k)+1)/(n-k)}.
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CROSSREFS
| Sequence in context: A115055 A158468 A200770 * A128504 A193822 A202699
Adjacent sequences: A100049 A100050 A100051 * A100053 A100054 A100055
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 31 2004
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