Triangle of characteristic polynomials, see Mathematica code.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =-4a(4) =-1a(5) =1a(6) =-36a(7) =9a(8) =5a(9) =-1a(10) =576a(11) =64a(12) =-61a(13) =-5a(14) =1a(15) =14400a(16) =-1600a(17) =-1045a(18) =105a(19) =14a(20) =-1a(21) =-518400a(22) =-32400a(23) =29088a(24) =1593a(25) =-385a(26) =-14a(27) =1a(28) =-25401600a(29) =1587600