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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =10a(5) =40a(6) =154a(7) =590a(8) =2262a(9) =8688a(10) =33440a(11) =128988a(12) =498576a(13) =1930864a(14) =7491054a(15) =29109782a(16) =113286470a(17) =441472864a(18) =1722528144a(19) =6728523772a(20) =26310196060a(21) =102977710064a(22) =403408546644