Triangle with T(n,k)=n!*(k-1)^k/k! where 1<=k<=n.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =3a(5) =8a(6) =0a(7) =12a(8) =32a(9) =81a(10) =0a(11) =60a(12) =160a(13) =405a(14) =1024a(15) =0a(16) =360a(17) =960a(18) =2430a(19) =6144a(20) =15625a(21) =0a(22) =2520a(23) =6720a(24) =17010a(25) =43008a(26) =109375a(27) =279936a(28) =0a(29) =20160