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

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =3a(5) =7a(6) =1a(7) =3a(8) =8a(9) =15a(10) =1a(11) =3a(12) =9a(13) =22a(14) =31a(15) =1a(16) =3a(17) =10a(18) =31a(19) =63a(20) =63a(21) =1a(22) =3a(23) =11a(24) =42a(25) =117a(26) =185a(27) =127a(28) =1a(29) =3