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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =1a(8) =3a(9) =1a(10) =1a(11) =1a(12) =7a(13) =5a(14) =1a(15) =1a(16) =1a(17) =13a(18) =13a(19) =11a(20) =1a(21) =1a(22) =1a(23) =21a(24) =25a(25) =55a(26) =21a(27) =1a(28) =1a(29) =1