G.f. satisfies: A(x) = x + A(A(A(A(x)^2))).

Terms

a(0) =1a(1) =1a(2) =2a(3) =8a(4) =32a(5) =138a(6) =624a(7) =2922a(8) =14036a(9) =68788a(10) =342584a(11) =1728812a(12) =8820864a(13) =45428616a(14) =235846688a(15) =1232970010a(16) =6485204532a(17) =34295308230a(18) =182233431688a(19) =972493015258