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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =7a(5) =1a(6) =1a(7) =61a(8) =61a(9) =1a(10) =1a(11) =601a(12) =1561a(13) =601a(14) =1a(15) =1a(16) =6721a(17) =36121a(18) =36121a(19) =6721a(20) =1a(21) =1a(22) =85681a(23) =856801a(24) =1738801a(25) =856801a(26) =85681a(27) =1a(28) =1a(29) =1239841