Array read by antidiagonals: T(n, k) = ((n+4)^k-(n-1)^k)/5.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =1a(5) =3a(6) =0a(7) =1a(8) =5a(9) =13a(10) =0a(11) =1a(12) =7a(13) =25a(14) =51a(15) =0a(16) =1a(17) =9a(18) =43a(19) =125a(20) =205a(21) =0a(22) =1a(23) =11a(24) =67a(25) =259a(26) =625a(27) =819a(28) =0a(29) =1