a(1)=1, a(n)=ceiling(n*(a(n-1)+3/a(n-1))).

Terms

a(0) =1a(1) =8a(2) =26a(3) =105a(4) =526a(5) =3157a(6) =22100a(7) =176801a(8) =1591210a(9) =15912101a(10) =175033112a(11) =2100397345a(12) =27305165486a(13) =382272316805