G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =15a(5) =47a(6) =153a(7) =514a(8) =1769a(9) =6205a(10) =22102a(11) =79733a(12) =290721a(13) =1069688a(14) =3966739a(15) =14810348a(16) =55627778a(17) =210046102a(18) =796864028a(19) =3035912900a(20) =11610468138a(21) =44556451207a(22) =171529074168a(23) =662238211929