Summed lengths of nonintersecting rook paths on an n X k board (square array by antidiagonals).

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =4a(5) =2a(6) =3a(7) =14a(8) =14a(9) =3a(10) =4a(11) =40a(12) =64a(13) =40a(14) =4a(15) =5a(16) =104a(17) =284a(18) =284a(19) =104a(20) =5a(21) =6a(22) =256a(23) =1206a(24) =1912a(25) =1206a(26) =256a(27) =6a(28) =7a(29) =608