Triangle of coefficients of polynomials enumerating trees with n labeled nodes by inversions.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =6a(5) =6a(6) =3a(7) =1a(8) =24a(9) =36a(10) =30a(11) =20a(12) =10a(13) =4a(14) =1a(15) =120a(16) =240a(17) =270a(18) =240a(19) =180a(20) =120a(21) =70a(22) =35a(23) =15a(24) =5a(25) =1a(26) =720a(27) =1800a(28) =2520a(29) =2730