G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^3) )^2.

Terms

a(0) =1a(1) =2a(2) =3a(3) =14a(4) =55a(5) =226a(6) =1042a(7) =4840a(8) =23103a(9) =113118a(10) =561568a(11) =2826550a(12) =14392534a(13) =73967650a(14) =383271596a(15) =2000096144a(16) =10502029735a(17) =55446004880a(18) =294155761676