a(n) = -Sum_{k = 0..n-1} (n+k)!a(k)/(2k)!.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =1a(4) =-1a(5) =-17a(6) =-107a(7) =-415a(8) =1231a(9) =56671a(10) =924365a(11) =11322001a(12) =97495687a(13) =-78466897a(14) =-31987213451