Rook polynomials.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =24a(5) =44a(6) =80a(7) =144a(8) =264a(9) =484a(10) =888a(11) =1632a(12) =3000a(13) =5516a(14) =10144a(15) =18656a(16) =34312a(17) =63108a(18) =116072a(19) =213488a(20) =392664a(21) =722220a(22) =1328368a(23) =2443248a(24) =4493832a(25) =8265444a(26) =15202520a(27) =27961792a(28) =51429752a(29) =94594060