a(n) = Sum_{k=0..n} (-1)^(n-k)*floor(sqrt(Bell(k))).

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =2a(5) =5a(6) =9a(7) =20a(8) =44a(9) =101a(10) =239a(11) =584a(12) =1468a(13) =3789a(14) =10027a(15) =27161a(16) =75211a(17) =212651a(18) =613228a(19) =1801879a(20) =5390071a(21) =16401436a(22) =50730640a(23) =159393146a(24) =508408373a(25) =1645330314a(26) =5399614435a(27) =17960973056a(28) =60528130675