G.f.: 2 - x*2/(1 - (1-8*x)^(1/4)).

Terms

a(0) =1a(1) =3a(2) =5a(3) =20a(4) =101a(5) =572a(6) =3470a(7) =22040a(8) =144669a(9) =973356a(10) =6676186a(11) =46503080a(12) =328034226a(13) =2338460056a(14) =16819478972a(15) =121903180848a(16) =889396747869