%I A049061
%S A049061 1,1,1,1,0,1,1,1,1,1,1,2,6,2,1,1,1,8,8,1,1,1,8,19,0,19,8,1,
%T A049061 1,7,27,19,19,27,7,1,1,22,32,86,190,86,32,22,1,1,21,54,54,276,
%U A049061 276,54,54,21,1,1,52,27,648,1002,0,1002,648,27,52,1,1,51,25
%V A049061 1,1,-1,1,0,-1,1,-1,-1,1,1,2,-6,2,1,1,1,-8,8,-1,-1,1,8,-19,0,19,-8,-1,
%W A049061 1,7,-27,19,19,-27,7,1,1,22,-32,-86,190,-86,-32,22,1,1,21,-54,-54,276,
%X A049061 -276,54,54,-21,-1,1,52,27,-648,1002,0,-1002,648,-27,-52,-1,1,51,-25
%N A049061 Triangle a(n,k) (1<=k<=n) of "signed Eulerian numbers" read by rows.
%C A049061 Identical to rows n=2..n of D(n,k) on page 2 of Tanimoto reference. - 
               Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 11 2006
%D A049061 Desarmenien, Jacques; Foata, Dominique; The signed Eulerian numbers. 
               Discrete Math. 99 (1992), number 1-3, 49-58.
%H A049061 J. Desarmenien and D. Foata, <a href="http://www-irma.u-strasbg.fr/~foata/
               paper/pub62.html">The signed Eulerian Numbers</a>
%H A049061 Shinji Tanimoto, <a href="http://arXiv.org/abs/math/0612135">Parity-Alternate 
               Permutations and Signed Eulerian Numbers</a>, math.CO/0612135.
%H A049061 S. Tanimoto, <a href="http://arXiv.org/abs/math.CO/0602263">A new approach 
               to signed Eulerian numbers</a>
%F A049061 a(2n, k)=a(2n-1, k)-a(2n-1, k-1), a(2n+1, k) = k*a(2n, k)+(2n-k+2)*a(2n, 
               k-1).
%e A049061 1; 1,-1; 1,0,-1; 1,-1,-1,1; 1,2,-6,2,1; ...
%Y A049061 Cd. A008292.
%Y A049061 Sequence in context: A134301 A004544 A010590 this_sequence A082516 A008905 
               A136760
%Y A049061 Adjacent sequences: A049058 A049059 A049060 this_sequence A049062 A049063 
               A049064
%K A049061 sign,easy,tabl,nice
%O A049061 1,12
%A A049061 N. J. A. Sloane (njas(AT)research.att.com).
%E A049061 More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2000
%E A049061 ArXiv URL replaced by its non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 23 2009