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

Terms

a(0) =1a(1) =2a(2) =3a(3) =12a(4) =49a(5) =218a(6) =1037a(7) =5106a(8) =25909a(9) =134410a(10) =709691a(11) =3801498a(12) =20606654a(13) =112828202a(14) =623087675a(15) =3466539248a(16) =19411070496a(17) =109313442562a(18) =618713495451