Array read by antidiagonals: T(n, k) = ((n+2)^k-(n-1)^k)/3.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =0a(7) =1a(8) =3a(9) =3a(10) =0a(11) =1a(12) =5a(13) =9a(14) =5a(15) =0a(16) =1a(17) =7a(18) =21a(19) =27a(20) =11a(21) =0a(22) =1a(23) =9a(24) =39a(25) =85a(26) =81a(27) =21a(28) =0a(29) =1