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

Terms

a(0) =1a(1) =2a(2) =6a(3) =24a(4) =114a(5) =600a(6) =3372a(7) =19824a(8) =120422a(9) =749848a(10) =4760228a(11) =30688560a(12) =200338740a(13) =1321408656a(14) =8791205496a(15) =58912586784a(16) =397228820742