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

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =0a(6) =0a(7) =12a(8) =12a(9) =0a(10) =0a(11) =216a(12) =484a(13) =216a(14) =0a(15) =0a(16) =5760a(17) =21000a(18) =21000a(19) =5760a(20) =0a(21) =0a(22) =216000a(23) =1117920a(24) =1822500a(25) =1117920a(26) =216000a(27) =0a(28) =0a(29) =10886400