a(1)=a(2)=a(3)=1; for n>3, a(n)=(a(n-1)*a(n-2)+a(n-1)+a(n-2))/a(n-3).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =31a(6) =85a(7) =393a(8) =1093a(9) =5071a(10) =14119a(11) =65523a(12) =182449a(13) =846721a(14) =2357713a(15) =10941843a(16) =30467815a(17) =141397231a(18) =393723877a(19) =1827222153a(20) =5087942581a(21) =23612490751a(22) =65749529671a(23) =305135157603a(24) =849655943137