a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 2.

Terms

a(0) =2a(1) =5a(2) =11a(3) =26a(4) =56a(5) =122a(6) =287a(7) =677a(8) =1457a(9) =3137a(10) =6833a(11) =14885a(12) =35015a(13) =82370a(14) =194300a(15) =458330a(16) =986390a(17) =2122850a(18) =4570610a(19) =9840770a(20) =21435122a(21) =46689890a(22) =101709206a(23) =221563226a(24) =521198276a(25) =1226050226a(26) =2884185551a(27) =6784816901a(28) =16004491001a(29) =37752490001