Coefficient triangle of permutation-based polynomials: p(x,n)=Product[x - n!/(n - i)!, {i, 0, n}].

Terms

a(0) =1a(1) =-1a(2) =1a(3) =1a(4) =-2a(5) =1a(6) =-4a(7) =8a(8) =-5a(9) =1a(10) =108a(11) =-180a(12) =87a(13) =-16a(14) =1a(15) =-27648a(16) =39168a(17) =-12912a(18) =1456a(19) =-65a(20) =1a(21) =86400000a(22) =-110880000a(23) =26094000a(24) =-1650400a(25) =36725a(26) =-326a(27) =1a(30) =-896020704000a(31) =34174310400