A symmetrical triangle sequence: t(n,m)=n!*Eulerian[n + 1, m]^2 - n! + 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =31a(5) =1a(6) =1a(7) =721a(8) =721a(9) =1a(10) =1a(11) =16201a(12) =104521a(13) =16201a(14) =1a(15) =1a(16) =389761a(17) =10944361a(18) =10944361a(19) =389761a(20) =1a(21) =1a(22) =10367281a(23) =1021305601a(24) =4202679601a(25) =1021305601a(26) =10367281a(27) =1a(28) =1a(29) =307480321