A generalization of triangles A071951 (Legendre-Stirling) and A089504.

Terms

a(0) =1a(1) =24a(2) =1a(3) =576a(4) =144a(5) =1a(6) =13824a(7) =17856a(8) =504a(9) =1a(10) =331776a(11) =2156544a(12) =199296a(13) =1344a(14) =1a(15) =7962624a(16) =259117056a(17) =73903104a(18) =1328256a(19) =3024a(20) =1a(21) =191102976a(22) =31102009344a(23) =26864234496a(24) =1189638144a(25) =6408576a(26) =6048a(27) =1a(28) =4586471424a(32) =11956045824