Antidiagonal expansion of the polynomials: f(x,n) = 1/(exp(t) - Sum_{i=1..n} t^i/i!).

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =0a(5) =-3a(6) =1a(7) =0a(8) =0a(9) =-4a(10) =1a(11) =0a(12) =0a(13) =-4a(14) =25a(15) =1a(16) =0a(17) =0a(18) =0a(19) =-5a(20) =114a(21) =1a(22) =0a(23) =0a(24) =0a(25) =-5a(26) =-6a(27) =-287a(28) =1a(29) =0