Rook polynomials.

Terms

a(0) =1a(1) =4a(2) =18a(3) =96a(4) =265a(5) =672a(6) =1617a(7) =3776a(8) =8577a(9) =19080a(10) =41745a(11) =90048a(12) =191945a(13) =404992a(14) =846945a(15) =1757440a(16) =3621697a(17) =7417800a(18) =15109313a(19) =30623520a(20) =61788489a(21) =124158496a(22) =248549937a(23) =495852480a(24) =986076225a(25) =1955203016a(26) =3866245425a(27) =7625813888a(28) =15005718153