%I A037012
%S A037012 0,1,1,1,0,1,1,1,1,1,1,2,0,2,1,1,3,2,2,3,1,1,4,5,0,5,4,1,
%T A037012 1,5,9,5,5,9,5,1,1,6,14,14,0,14,14,6,1,1,7,20,28,14,14,28,
%U A037012 20,7,1,1,8,27,48,42,0,42,48,27,8,1,1,9,35,75,90,42,42,90
%V A037012 0,1,-1,1,0,-1,1,1,-1,-1,1,2,0,-2,-1,1,3,2,-2,-3,-1,1,4,5,0,-5,-4,-1,
%W A037012 1,5,9,5,-5,-9,-5,-1,1,6,14,14,0,-14,-14,-6,-1,1,7,20,28,14,-14,-28,
%X A037012 -20,-7,-1,1,8,27,48,42,0,-42,-48,-27,-8,-1,1,9,35,75,90,42,-42,-90
%N A037012 Coefficients in expansion of (1-x)(1+x)^(n-1), n>0.
%D A037012 A. A. Kirillov, Variations on the triangular theme, Amer. Math. Soc. 
               Transl., (2), Vol. 169, 1995, pp. 43-73, see p. 71.
%F A037012 T(n, k)=T(n-1, k-1)+T(n-1, k); T(0, 0)=0, T(1, 0)=1, T(1, 1)=-1.
%F A037012 T(n, k)=C(n, k)-C(n, k-1) where C = binomial coefficient A007318.
%F A037012 G.f.: (1-y) / (1-x-xy). - R. Stephan, Jan 23 2005
%e A037012 0; 1 -1; 1 0 -1; 1 1 -1 -1; 1 2 0 -2 -1; 1 3 2 -2 -3 -1; ...
%o A037012 (PARI) T(n,k)=if(n<1,0,polcoeff((1-x)*(1+x)^(n-1),k))
%Y A037012 Skew analogue of Pascal's triangle A007318, central column gives Catalan 
               numbers A000108, essentially same as A008482, except rows are read 
               from left to right (A037012 = - this sequence).
%Y A037012 Apart from initial term, same as A080232.
%Y A037012 Sequence in context: A061398 A080232 A008482 this_sequence A112467 A112466 
               A166348
%Y A037012 Adjacent sequences: A037009 A037010 A037011 this_sequence A037013 A037014 
               A037015
%K A037012 sign,easy,tabl
%O A037012 0,12
%A A037012 N. J. A. Sloane (njas(AT)research.att.com), Michael Somos.