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

Terms

a(0) =1a(1) =1a(2) =0a(3) =-1a(4) =0a(5) =3a(6) =2a(7) =-9a(8) =-12a(9) =35a(10) =78a(11) =-153a(12) =-544a(13) =723a(14) =4170a(15) =-3337a(16) =-35028a(17) =10851a(18) =320678a(19) =57255a(20) =-3178152a(21) =-2190253a(22) =33864546a(23) =42120183a(24) =-385314460a(25) =-719159517a(26) =4649508222a(27) =12033407591a(28) =-59076411312a(29) =-204022615725