G.f. satisfies A(x) = x/(1-x) + Sum_{n>=1} A(x^n)^2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =16a(4) =53a(5) =201a(6) =775a(7) =3156a(8) =13123a(9) =55915a(10) =241989a(11) =1062626a(12) =4718381a(13) =21157587a(14) =95652899a(15) =435556794a(16) =1995707807a(17) =9194783480a(18) =42570402239a(19) =197957963454a(20) =924157499417