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A087960
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(-1)^binomial(n+1,2).
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9
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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, Aug 10 2009]
The Kn22 sums, see A180662, of triangle A108299 equal the terms of this sequence. [Johannes W. Meijer, Aug 14 2011]
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FORMULA
| a(n) = (-1)^A000217(n).
a(n) = (-1)^floor((n+1)/2) - Benoit Cloitre and Ray Chandler, Sep 19 2003
a(n) = -(i^(1-n)-i^(-n)-i^(n)+i^(n-1))/2, with i=sqrt(-1). - Paolo P. Lava, Jun 28 2006, corrected R. J. Mathar, Sep 25 2009
a(n) = cos(n*Pi/2)-sin(n*Pi/2) - Paolo P. Lava, Aug 02 2006, and R. J. mathar, Sep 25 2009
G.f.: (1-x)/(1+x^2). - Paul Barry, Aug 10 2009
a(n) = i^(n(n+1)). - Bruno Berselli, Oct 17 2011
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EXAMPLE
| a(1) = -1 since (-1)^binomial(2,2) = (-1)^1 = -1
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CROSSREFS
| Cf. A021913, A057077.
Sequence in context: A158387 A008836 * A164660 A106400 A112865 A114523
Adjacent sequences: A087957 A087958 A087959 * A087961 A087962 A087963
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KEYWORD
| sign,easy
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AUTHOR
| W. Edwin Clark (eclark(AT)math.usf.edu), Sep 17 2003
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EXTENSIONS
| More terms from Benoit Cloitre and Ray Chandler, Sep 19 2003
Offset and vandermonde formula corrected by R. J. Mathar, Sep 25 2009
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