G.f. satisfies A(x) = 1/(1 - x*(1 + x*A(x))^2).

Terms

a(0) =1a(1) =1a(2) =3a(3) =8a(4) =25a(5) =81a(6) =274a(7) =953a(8) =3389a(9) =12265a(10) =45025a(11) =167256a(12) =627540a(13) =2374672a(14) =9052447a(15) =34731401a(16) =134010573a(17) =519683813a(18) =2024370167a(19) =7917605996a(20) =31080085431a(21) =122407860927a(22) =483558273368