Triangle, row sums = a signed, shifted version of A000587, the Rao Uppuluri-Carpenter numbers.

Terms

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