Array read by ascending antidiagonals: A(n,k) = n! * [x^n] 1/(1 - x*exp(x))^k.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =0a(7) =4a(8) =2a(9) =1a(10) =0a(11) =21a(12) =10a(13) =3a(14) =1a(15) =0a(16) =148a(17) =66a(18) =18a(19) =4a(20) =1a(21) =0a(22) =1305a(23) =560a(24) =141a(25) =28a(26) =5a(27) =1a(28) =0a(29) =13806