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

Terms

a(0) =1a(1) =3a(2) =7a(3) =16a(4) =38a(5) =95a(6) =249a(7) =678a(8) =1901a(9) =5451a(10) =15906a(11) =47066a(12) =140868a(13) =425657a(14) =1296665a(15) =3977684a(16) =12276617a(17) =38094013a(18) =118768915a(19) =371875752a(20) =1168843808a(21) =3686549845a(22) =11664123048a(23) =37011249678a(24) =117750111763a(25) =375529083267