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

Terms

a(0) =1a(1) =4a(2) =13a(3) =53a(4) =266a(5) =1597a(6) =11180a(7) =89441a(8) =804970a(9) =8049701a(10) =88546712a(11) =1062560545a(12) =13813287086a(13) =193386019205