A Catalan transform of [x^n](1/(1-2x-2x^2)) (A002605).

Terms

a(0) =1a(1) =2a(2) =8a(3) =32a(4) =132a(5) =552a(6) =2328a(7) =9872a(8) =42020a(9) =179336a(10) =766888a(11) =3284272a(12) =14081224a(13) =60426576a(14) =259490736a(15) =1114965792a(16) =4792924356a(17) =20611174920a(18) =88662405768a(19) =381494338032