G.f. A(x) satisfies A(x)^2 = A( x^2 + 2*x*A(x)^2 + 2*A(x)^4 ).

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =39a(5) =161a(6) =699a(7) =3135a(8) =14427a(9) =67716a(10) =322959a(11) =1560585a(12) =7624007a(13) =37593476a(14) =186856061a(15) =935214523a(16) =4709265692a(17) =23841104525a(18) =121275951719a(19) =619558165489