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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =15a(5) =1a(6) =1a(7) =193a(8) =193a(9) =1a(10) =1a(11) =2473a(12) =9481a(13) =2473a(14) =1a(15) =1a(16) =34081a(17) =362281a(18) =362281a(19) =34081a(20) =1a(21) =1a(22) =517681a(23) =12862081a(24) =34789681a(25) =12862081a(26) =517681a(27) =1a(28) =1a(29) =8709121