A049689 a(n)=Sum{((-1)^(i+1))*T(i,n-i): i=0,1,...,n}, array T as in A049687.

0, 0, 1, 0, 3, 0, 5, 0, 9, 0, 13, 0, 17, 0, 23, 0, 31, 0, 37, 0, 45, 0, 55, 0, 63, 0, 75, 0, 87, 0, 95, 0, 111, 0, 127, 0, 139, 0, 157, 0, 173, 0