Rook polynomials.

Terms

a(0) =1a(1) =9a(2) =72a(3) =320a(4) =1185a(5) =3892a(6) =11776a(7) =33480a(8) =90745a(9) =236808a(10) =599112a(11) =1477216a(12) =3564001a(13) =8439960a(14) =19666688a(15) =45183824a(16) =102520881a(17) =230046452a(18) =511085960a(19) =1125313056a(20) =2457641857a(21) =5327760940a(22) =11471647872a(23) =24547187800a(24) =52225646057a(25) =110524638672