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%I #2 Mar 30 2012 18:59:13
%S 1,1,-1,-1,0,1,0,0,1,-1,0,-1,0,0,1,0,0,0,0,1,-1,0,0,-1,0,0,0,1,0,0,0,
%T 0,0,0,1,-1,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,-1,0,0,0,
%U 0,0,1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0
%N Number triangle (1,-x)+(x,x)/2+(x,-x)/2-(x^2,x^2) (expressed using the notation of stretched Riordan arrays).
%C Row sums are A000007. Diagonal sums are A115525. Matrix inverse is A115526. Row sums of inverse are A023416(n+2).
%F Column k has g.f. (-x)^k+(x(-x)^k+x^(k+1))/2-x^(2k+2); Number triangle T(n, k)=(-1)^n*(if(n=k, 1, 0) OR if(n=2k+2, -1, 0) OR if(n=k+1, -(1+(-1)^k)/2, 0)).
%F G.f.: (1+x-x*y)/(1-x^2*y^2)-x^2/(1-x^2*y); - _Paul Barry_, Feb 02 2006
%e Triangle begins
%e 1,
%e 1, -1,
%e -1, 0, 1,
%e 0, 0, 1, -1,
%e 0, -1, 0, 0, 1,
%e 0, 0, 0, 0, 1, -1,
%e 0, 0, -1, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 1, -1,
%e 0, 0, 0, -1, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
%e 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
%e 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
%K easy,sign,tabl
%O 0,1
%A _Paul Barry_, Jan 25 2006
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