Search: id:A087960
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%I A087960
%S A087960 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,
%T A087960 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,
%U A087960 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
%V A087960 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,
%W A087960 -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,
%X A087960 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
%N A087960 (-1)^binomial(n+1,2).
%C A087960 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).
%C A087960 Hankel transform of A097331, A097332. [From Paul Barry (pbarry(AT)wit.ie), 
               Aug 10 2009]
%F A087960 a(n) = (-1)^A000217(n).
%F A087960 a(n) = (-1)^floor((n+1)/2) - Benoit Cloitre (benoit7848c(AT)orange.fr) 
               and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 19 2003
%F A087960 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
%F A087960 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
%F A087960 G.f.: (1-x)/(1+x^2). [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
%e A087960 a(1) = -1 since (-1)^binomial(2,2) = (-1)^1 = -1
%Y A087960 Cf. A021913, A057077.
%Y A087960 Sequence in context: A063747 A077008 A158387 this_sequence A164660 A114523 
               A000012
%Y A087960 Adjacent sequences: A087957 A087958 A087959 this_sequence A087961 A087962 
               A087963
%K A087960 easy,sign
%O A087960 0,1
%A A087960 W. Edwin Clark (eclark(AT)math.usf.edu), Sep 17 2003
%E A087960 More terms from Benoit Cloitre (benoit7848c(AT)orange.fr) and Ray Chandler 
               (rayjchandler(AT)sbcglobal.net), Sep 19 2003
%E A087960 Offset and vandermonde formula corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 25 2009

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