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

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =11a(5) =23a(6) =52a(7) =120a(8) =247a(9) =534a(10) =1433a(11) =2540a(12) =3264a(13) =30169a(14) =19123a(15) =-363258a(16) =2951500a(17) =-1601367a(18) =-99325484a(19) =799655132a(20) =-1194225728a(21) =-32599353806a(22) =345568196667