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

Terms

a(0) =1a(1) =3a(2) =9a(3) =34a(4) =147a(5) =684a(6) =3341a(7) =16896a(8) =87702a(9) =464566a(10) =2501178a(11) =13646625a(12) =75289022a(13) =419301351a(14) =2354121750a(15) =13309905653a(16) =75715795119a(17) =433063793430