a(n) = 2*C(n) - 1, where C(n) = A000108(n) are the Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =27a(5) =83a(6) =263a(7) =857a(8) =2859a(9) =9723a(10) =33591a(11) =117571a(12) =416023a(13) =1485799a(14) =5348879a(15) =19389689a(16) =70715339a(17) =259289579a(18) =955277399a(19) =3534526379a(20) =13128240839a(21) =48932534039a(22) =182965127279a(23) =686119227299