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Search: id:A087960
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| 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Also equal to the sign of product(j-i, 1<=j<i<=n+1) = the sign of the vandermonde determinant for -1, -2, . . ., -(n+1).
Hankel transform of A097331, A097332. [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
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FORMULA
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a(n) = (-1)^A000217(n).
a(n) = (-1)^floor((n+1)/2) - Benoit Cloitre (benoit7848c(AT)orange.fr) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 19 2003
a(n) = -(i^(1-n)-i^(-n)-i^(n)+i^(n-1))/2, with i=(-1)^.5 - Paolo P. Lava (ppl(AT)spl.at), Jun 28 2006, corrected R. J. Mathar, Sep 25 2009
a(n)= cos(n*Pi/2)-sin(n*Pi/2) - Paolo P. Lava (ppl(AT)spl.at), Aug 02 2006, R. J. mathar, Sep 25 2009
G.f.: (1-x)/(1+x^2). [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
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EXAMPLE
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a(1) = -1 since (-1)^binomial(2,2) = (-1)^1 = -1
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CROSSREFS
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Cf. A021913, A057077.
Sequence in context: A063747 A077008 A158387 this_sequence A164660 A114523 A000012
Adjacent sequences: A087957 A087958 A087959 this_sequence A087961 A087962 A087963
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KEYWORD
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easy,sign
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AUTHOR
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W. Edwin Clark (eclark(AT)math.usf.edu), Sep 17 2003
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 19 2003
Offset and vandermonde formula corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 25 2009
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