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

Terms

a(0) =1a(1) =2a(2) =3a(3) =10a(4) =29a(5) =92a(6) =314a(7) =1078a(8) =3830a(9) =13844a(10) =50746a(11) =188554a(12) =707667a(13) =2679960a(14) =10227940a(15) =39294772a(16) =151859858a(17) =589943516a(18) =2302462140a(19) =9023681820a(20) =35498194465a(21) =140122652960a(22) =554827907272