Regular triangle of certain polynomial expansion coefficients for the n-th power series.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =-2a(5) =2a(6) =0a(7) =5a(8) =-10a(9) =6a(10) =1a(11) =-10a(12) =40a(13) =-54a(14) =24a(15) =0a(16) =21a(17) =-140a(18) =336a(19) =-336a(20) =120a(21) =1a(22) =-42a(23) =462a(24) =-1764a(25) =3024a(26) =-2400a(27) =720a(28) =0a(29) =85