a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^k.

Terms

a(0) =1a(1) =3a(2) =12a(3) =62a(4) =327a(5) =1851a(6) =10802a(7) =64440a(8) =391218a(9) =2408001a(10) =14989608a(11) =94197594a(12) =596756374a(13) =3807010920a(14) =24435261432a(15) =157681777148