Array read by ascending antidiagonals, A(n, k) = -(-n)^k*FallingFactorial(1/n, k) for n, k >= 1.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =1a(5) =0a(6) =1a(7) =2a(8) =3a(9) =0a(10) =1a(11) =3a(12) =10a(13) =15a(14) =0a(15) =1a(16) =4a(17) =21a(18) =80a(19) =105a(20) =0a(21) =1a(22) =5a(23) =36a(24) =231a(25) =880a(26) =945a(27) =0a(28) =1a(29) =6