A122536(2n)/2.

Terms

a(0) =1a(1) =3a(2) =10a(3) =37a(4) =143a(5) =562a(6) =2230a(7) =8884a(8) =35465a(9) =141720a(10) =566600a(11) =2265843a(12) =9062261a(13) =36246826a(14) =144982872a(15) =579922629a(16) =2319672806a(17) =9278655812a(18) =37114552436a(19) =148458068139a(20) =593831989359