%I #9 Jan 17 2014 04:25:44

%S 1,0,1,1,0,1,0,0,0,1,1,0,-1,0,1,0,-1,0,-2,0,1,1,0,-2,0,-3,0,1,0,-2,0,

%T -2,0,-4,0,1,1,0,-2,0,-1,0,-5,0,1,0,-3,0,0,0,1,0,-6,0,1,1,0,-1,0,3,0,

%U 4,0,-7,0,1,0,-4,0,3,0,6,0,8,0,-8,0,1,1,0,1,0,6,0,8,0,13,0,-9,0,1

%N Riordan array (1/(1-x^2),x(1-2x^2)/(1-x^2)).

%C Row sums are A077948.

%C Diagonal sums are the aerated version of A009545 with g.f. 1/(1-2x^2+2x^4).

%F Number triangle T(n,k)=sum{j=0..n-k, C(j-(n-k)/2-1,j)C(k,j)(1+(-1)^(n-k))/2}

%F T(n,k)=T(n-1,k-1)+T(n-2,k)-2*T(n-3,k-1), T(0,0)=T(1,1)=T(2,0)=T(2,2)=1, T(1,1)=T(2,1)=0, T(n,k)=0 if k<0 or if k>n. - _Philippe Deléham_, Jan 16 2014

%e Triangle begins

%e 1,

%e 0, 1,

%e 1, 0, 1,

%e 0, 0, 0, 1,

%e 1, 0, -1, 0, 1,

%e 0, -1, 0, -2, 0, 1,

%e 1, 0, -2, 0, -3, 0, 1,

%e 0, -2, 0, -2, 0, -4, 0, 1

%K easy,sign,tabl

%O 0,19

%A _Paul Barry_, Mar 09 2006