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

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =83a(5) =363a(6) =1733a(7) =8942a(8) =49484a(9) =291871a(10) =1825501a(11) =12054705a(12) =83734241a(13) =609851830a(14) =4644041462a(15) =36883843101a(16) =304846039251