Coefficient triangle for polynomials used for e.g.f.s for unsigned Stirling1 diagonals.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =3a(6) =6a(7) =26a(8) =35a(9) =15a(10) =24a(11) =154a(12) =340a(13) =315a(14) =105a(15) =120a(16) =1044a(17) =3304a(18) =4900a(19) =3465a(20) =945a(21) =720a(22) =8028a(23) =33740a(24) =70532a(25) =78750a(26) =45045a(27) =10395a(28) =5040a(29) =69264