Triangle T(n, k) = binomial(n, k)*A000166(n-k)*k^n with T(0, 0) = 1, read by rows.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =0a(5) =4a(6) =0a(7) =3a(8) =0a(9) =27a(10) =0a(11) =8a(12) =96a(13) =0a(14) =256a(15) =0a(16) =45a(17) =640a(18) =2430a(19) =0a(20) =3125a(21) =0a(22) =264a(23) =8640a(24) =29160a(25) =61440a(26) =0a(27) =46656a(28) =0a(29) =1855