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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =2a(8) =2a(9) =1a(10) =1a(11) =4a(12) =5a(13) =2a(14) =1a(15) =1a(16) =8a(17) =14a(18) =8a(19) =3a(20) =1a(21) =1a(22) =16a(23) =41a(24) =32a(25) =13a(26) =3a(27) =1a(28) =1a(29) =32