Array read by ascending antidiagonals: A(n, k) = Sum_{j=0..n} binomial(k, j)*|Stirling1(n, j)|.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =0a(7) =1a(8) =2a(9) =1a(10) =0a(11) =2a(12) =3a(13) =3a(14) =1a(15) =0a(16) =6a(17) =7a(18) =6a(19) =4a(20) =1a(21) =0a(22) =24a(23) =23a(24) =16a(25) =10a(26) =5a(27) =1a(28) =0a(29) =120