Expansion of e.g.f. arctan(x)*exp(x).

Terms

a(0) =0a(1) =1a(2) =2a(3) =1a(4) =-4a(5) =9a(6) =110a(7) =-279a(8) =-4520a(9) =17265a(10) =322618a(11) =-1638031a(12) =-35226860a(13) =223578809a(14) =5463436134a(15) =-41639195623