Table by antidiagonals of T(n,k) = ((n+1)^k - (-n)^k)/(2*n+1).

Terms

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