a(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k), n>=1.

Terms

a(0) =1a(1) =3a(2) =13a(3) =39a(4) =126a(5) =477a(6) =1765a(7) =6495a(8) =24709a(9) =95128a(10) =367368a(11) =1431453a(12) =5620343a(13) =22170543a(14) =87858813a(15) =349708431a(16) =1397003136a(17) =5598513261a(18) =22502171771a(19) =90681323364a(20) =366299212873