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

Terms

a(0) =1a(1) =3a(2) =7a(3) =19a(4) =63a(5) =231a(6) =895a(7) =3615a(8) =15055a(9) =64111a(10) =277791a(11) =1220767a(12) =5427775a(13) =24371199a(14) =110350335a(15) =503289727a(16) =2309992959a(17) =10661634303a(18) =49452179455a(19) =230391918591