A(x) = C(x) * C(x^2) * C(x^4) * C(x^8) *...; C = Catalan, A000108.

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =19a(5) =50a(6) =158a(7) =492a(8) =1635a(9) =5466a(10) =18794a(11) =65332a(12) =230414a(13) =820052a(14) =2945436a(15) =10654808a(16) =38795523a(17) =142045610a(18) =522694866a(19) =1931912036a(20) =7169014298a(21) =26698782108a(22) =99756713732a(23) =373839656616