Array, read by antidiagonals, where A(n,k) = exp(-1)*Sum_{i>=0} (i+k)^n/i!.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =1a(6) =5a(7) =5a(8) =3a(9) =1a(10) =15a(11) =15a(12) =10a(13) =4a(14) =1a(15) =52a(16) =52a(17) =37a(18) =17a(19) =5a(20) =1a(21) =203a(22) =203a(23) =151a(24) =77a(25) =26a(26) =6a(27) =1a(28) =877a(29) =877