Expansions of the characteristic polynomials of certain matrices, see Mathematica code.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =-4a(4) =-1a(5) =1a(6) =-27a(7) =10a(8) =4a(9) =-1a(10) =256a(11) =43a(12) =-42a(13) =-4a(14) =1a(15) =3125a(16) =-686a(17) =-398a(18) =72a(19) =9a(20) =-1a(21) =-46656a(22) =-5885a(23) =5774a(24) =542a(25) =-180a(26) =-9a(27) =1a(28) =-823543a(29) =127282