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

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =11a(5) =24a(6) =52a(7) =112a(8) =251a(9) =574a(10) =1347a(11) =3242a(12) =7996a(13) =20202a(14) =52245a(15) =138200a(16) =373640a(17) =1031702a(18) =2907207a(19) =8353892a(20) =24460864a(21) =72931232a(22) =221265823a(23) =682632254a(24) =2140211338a(25) =6814954528a(26) =22027143227a(27) =72228405060a(28) =240154754720