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%I #2 Mar 30 2012 18:59:07
%S 1,-1,1,-1,0,1,1,-1,-1,1,0,0,-1,0,1,0,0,1,-1,-1,1,0,0,0,0,-1,0,1,0,0,
%T 0,0,1,-1,-1,1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,
%U 0,-1,0,1,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1
%N Inverse of number triangle A106465.
%C A 'mixed' sequence array : rows alternate between the rows of the sequence array for the sequence (1,0,-1,0,0,0...) and the sequence array for the sequence (1,-1,-1,1,0,0,0,...). Column 2k has g.f. x^2k(1-x-x^2+x^3); column 2k+1 has g.f. x^(2k+1)(1-x^2). Row sums are 0^n=binomial(0,n)=(1,0,0,0,....). Diagonal sums are (1,-1,0,1,0,-1,...) with g.f. (1-x+x^2)/(1+x^2).
%e Triangle begins
%e 1;
%e -1,1;
%e -1,0,1;
%e 1,-1,-1,1;
%e 0,0,-1,0,1;
%e 0,0,1,-1,1,1;
%e 0,0,0,0,-1,0,1;
%K sign,tabl
%O 0,1
%A _Paul Barry_, May 03 2005
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