G.f. satisfies A(x) = 1 + Sum_{n>=0} (x*A(x))^(2^n).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =26a(6) =72a(7) =204a(8) =594a(9) =1762a(10) =5318a(11) =16270a(12) =50360a(13) =157392a(14) =496016a(15) =1574432a(16) =5028962a(17) =16152194a(18) =52133154a(19) =169004450a(20) =550036778a(21) =1796512970a(22) =5886709502a(23) =19346204982a(24) =63751851400a(25) =210605429496a(26) =697337388556