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%I #12 Jan 13 2014 01:23:48
%S 1,-1,1,1,-1,1,-1,0,-1,1,1,2,-1,-1,1,-1,-5,5,-2,-1,1,1,9,-10,8,-3,-1,
%T 1,-1,-14,14,-14,11,-4,-1,1,1,20,-14,14,-17,14,-5,-1,1,-1,-27,6,0,9,
%U -19,17,-6,-1,1,1,35
%N Riordan array (1/(1+x), x(1+2x)/(1+x)^2).
%C Row sums are (-1)^n*F(n-1), the inverse binomial transform of F(n+1). Diagonal sums are A124342.
%F Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)*C(n,j)*C(k,j-k)}; T(n,k)=sum{j=0..n, (-1)^(j-k)*C(k,n-j)*C(n,j-k)}.
%F T(n,k)=T(n-1,k-1)-2*T(n-1,k)+2*T(n-2,k-1)-T(n-2,k), T(0,0)=1, T(1,0)=-1, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - _Philippe Deléham_, Jan 12 2014
%e Triangle begins
%e 1;
%e -1, 1;
%e 1, -1, 1;
%e -1, 0, -1, 1;
%e 1, 2, -1, -1, 1;
%e -1, -5, 5, -2, -1, 1;
%e 1, 9, -10, 8, -3, -1, 1;
%e -1, -14, 14, -14, 11, -4, -1, 1;
%e 1, 20, -14, 14, -17, 14, -5, -1, 1;
%K easy,sign,tabl
%O 0,12
%A _Paul Barry_, Oct 26 2006
%E More terms from _Philippe Deléham_, Dec 19 2011
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