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

Terms

a(0) =1a(1) =0a(2) =-2a(3) =-2a(4) =4a(5) =10a(6) =-4a(7) =-38a(8) =-22a(9) =114a(10) =188a(11) =-234a(12) =-914a(13) =-18a(14) =3376a(15) =3338a(16) =-9416a(17) =-21718a(18) =14416a(19) =96338a(20) =39274a(21) =-328558a(22) =-471344a(23) =795398a(24) =2586064a(25) =-517690a(26) =-10453424a(27) =-8272658a(28) =32186818a(29) =63596494