a(n) = Sum_{k=0..floor(n/3)} (-n)^k * binomial(n-2*k,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =-2a(4) =-7a(5) =-14a(6) =13a(7) =113a(8) =337a(9) =19a(10) =-2579a(11) =-10867a(12) =-9911a(13) =71852a(14) =431229a(15) =741181a(16) =-2178783a(17) =-20081708a(18) =-51012467a(19) =58414532a(20) =1061935641a(21) =3651310699a(22) =1841181a(23) =-62090909433a(24) =-279070619279a(25) =-250335322449