Triangle read by rows: T(n, k) = Sum_{i=0..k-2} (-1)^(i+2) * (k-i-1)^n * binomial(k,i).

Terms

a(0) =1a(1) =1a(2) =5a(3) =1a(4) =13a(5) =23a(6) =1a(7) =29a(8) =121a(9) =119a(10) =1a(11) =61a(12) =479a(13) =1081a(14) =719a(15) =1a(16) =125a(17) =1681a(18) =6719a(19) =10081a(20) =5039a(21) =1a(22) =253a(23) =5543a(24) =35281a(25) =90719a(26) =100801a(27) =40319a(28) =1a(29) =509