Binomial transform of 1,0,1,0,2,0,4,0,8,0,16,...

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =21a(6) =50a(7) =120a(8) =289a(9) =697a(10) =1682a(11) =4060a(12) =9801a(13) =23661a(14) =57122a(15) =137904a(16) =332929a(17) =803761a(18) =1940450a(19) =4684660a(20) =11309769a(21) =27304197a(22) =65918162a(23) =159140520a(24) =384199201a(25) =927538921a(26) =2239277042a(27) =5406093004a(28) =13051463049a(29) =31509019101