a(n) = (1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)).

Terms

a(0) =1a(1) =3a(2) =9a(3) =31a(4) =120a(5) =514a(6) =2407a(7) =12205a(8) =66491a(9) =386699a(10) =2388096a(11) =15589732a(12) =107165081a(13) =773106715a(14) =5836100685a(15) =45981026703a(16) =377230766908