G.f. satisfies A(x) = 1/(1-x)^2 + x^2*A(x)^4.

Terms

a(0) =1a(1) =2a(2) =4a(3) =12a(4) =45a(5) =182a(6) =779a(7) =3480a(8) =16005a(9) =75234a(10) =359893a(11) =1746268a(12) =8573477a(13) =42511646a(14) =212587561a(15) =1070897000a(16) =5429174465a(17) =27679933778a(18) =141829437174a(19) =729972918876