Triangle, read by rows, T(n, k) = Sum_{j=0..k} (-1)^j*(n+k)!/((n-j)!*(k-j)!*j!).

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =-3a(5) =-6a(6) =1a(7) =-8a(8) =10a(9) =80a(10) =1a(11) =-15a(12) =75a(13) =35a(14) =-1050a(15) =1a(16) =-24a(17) =231a(18) =-784a(19) =-2394a(20) =14112a(21) =1a(22) =-35a(23) =532a(24) =-3948a(25) =7770a(26) =69762a(27) =-170940a(28) =1a(29) =-48