a(1)=1; for n >= 2, a(n) = floor(n!/(Sum_{k=1..n-1} a(k))).

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =13a(5) =32a(6) =93a(7) =274a(8) =861a(9) =2830a(10) =9707a(11) =34662a(12) =128442a(13) =492747a(14) =1952714a(15) =7978537a(16) =33552502a(17) =145002884a(18) =643093018a(19) =2923285048a(20) =13604173759a(21) =64747674282a(22) =314856179539