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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =4a(5) =1a(6) =23a(7) =33a(8) =11a(9) =1a(10) =425a(11) =620a(12) =220a(13) =26a(14) =1a(15) =18129a(16) =26525a(17) =9520a(18) =1180a(19) =57a(20) =1a(21) =1721419a(22) =2519664a(23) =905765a(24) =113050a(25) =5649a(26) =120a(27) =1a(28) =353654167a(29) =517670461