Triangle T(n, k) = (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k), read by rows.

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =0a(6) =0a(7) =6a(8) =6a(9) =0a(10) =0a(11) =36a(12) =121a(13) =36a(14) =0a(15) =0a(16) =240a(17) =1750a(18) =1750a(19) =240a(20) =0a(21) =0a(22) =1800a(23) =23290a(24) =50625a(25) =23290a(26) =1800a(27) =0a(28) =0a(29) =15120