Number triangle T(n,k)=(-1)^(n-k)*[k<=n]*Product{i=k+1..n,Sum{j=0..i-1,F(j-1)}}.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =1a(4) =-1a(5) =1a(6) =-2a(7) =2a(8) =-2a(9) =1a(10) =6a(11) =-6a(12) =6a(13) =-3a(14) =1a(15) =-30a(16) =30a(17) =-30a(18) =15a(19) =-5a(20) =1a(21) =240a(22) =-240a(23) =240a(24) =-120a(25) =40a(26) =-8a(27) =1a(28) =-3120a(29) =3120