a(2n) = A001570(n), a(2n+1) = -A007654(n+1).

Terms

a(0) =1a(1) =-3a(2) =13a(3) =-48a(4) =181a(5) =-675a(6) =2521a(7) =-9408a(8) =35113a(9) =-131043a(10) =489061a(11) =-1825200a(12) =6811741a(13) =-25421763a(14) =94875313a(15) =-354079488a(16) =1321442641a(17) =-4931691075a(18) =18405321661a(19) =-68689595568a(20) =256353060613a(21) =-956722646883