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

Terms

a(0) =1a(1) =1a(2) =0a(3) =-8a(4) =-34a(5) =-74a(6) =0a(7) =736a(8) =3334a(9) =7606a(10) =0a(11) =-80464a(12) =-372436a(13) =-864772a(14) =0a(15) =9400192a(16) =43976774a(17) =103061158a(18) =0a(19) =-1137528688a(20) =-5355697084a(21) =-12623082284a(22) =0a(23) =140697113792a(24) =665238165916a(26) =0a(30) =0