Triangle T(n, k) = (-1)^n*StirlingS2(n, k)*StirlingS2(n, n-k), read by rows.

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =0a(6) =0a(7) =-3a(8) =-3a(9) =0a(10) =0a(11) =6a(12) =49a(13) =6a(14) =0a(15) =0a(16) =-10a(17) =-375a(18) =-375a(19) =-10a(20) =0a(21) =0a(22) =15a(23) =2015a(24) =8100a(25) =2015a(26) =15a(27) =0a(28) =0a(29) =-21