Triangle T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =3a(5) =4a(6) =0a(7) =7a(8) =32a(9) =27a(10) =0a(11) =15a(12) =176a(13) =405a(14) =256a(15) =0a(16) =31a(17) =832a(18) =3888a(19) =6144a(20) =3125a(21) =0a(22) =63a(23) =3648a(24) =30618a(25) =90112a(26) =109375a(27) =46656a(28) =0a(29) =127